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What does a perpendicular bisector of a triangle split into two congruent parts?
That will depend on what type of triangle it is as for example if it is an isosceles triangle then it will form two congruent right angle triangles.
Which of these can not form a perpendicular bisector?
Perpendicular bisector lines intersect at right angles
What conjectures in Classic or Euclidean Geometry have been proved from elementary axioms?
All the below listed conjectures (first letter C of Conjecture) can be proved using the Euclidean axioms of geometry. They can be used to teach or learn geometry. In this way one "discovers" the power of the Euglidean axioms.Some may be beyond this goal as they stand, as the definitions of key concepts is not included (e.g., centroid [C15], or "vertical" angle [C2], sometimes called a "right" angle.C1 Linear Pair: If two angles form a linear pair, then they are supplementary and total 180 degrees.C2 Vertical Angles: If two angles are vertical angles (right angles), then they are congruent.C3a Corresponding Angles: If two parallel lines are cut by a transversal, then the corresponding angles are congruent.C3b Alternate Interior Angles: If two parallel lines are cut by a transversal, then alternate interior angles are congruent.C3 Parallel Lines: If two parallel lines are cut by a transversal, then corresponding angles are congruent, alternate interior angles are congruent, and alternate exterior angles are congruent.C4 Converse of Parallel Lines: If two lines are cut by a transversal to form pairs of congruent corresponding angles, congruent interior angles, or congruent exterior angles, then the lines are parallel.C5 Perpendicular Bisector: If a point is on the perpendicular bisector of a segment, then it is equidistant from the endpoint.C6 Converse of Perpendicular Bisector: If a point is equidistant from the endpoints of a segment, then it is on the perpendicular bisector of the segment.C7 Shortest Distance: The shortest distance from a point to a line is measured along the perpendicular bisector from the point to the line.C8 Angle Bisector: If a point is on the bisector of an angle, then it is equidistant from the sides of the angle.C9 Angle Bisector Concurrency: The three angle bisectors of a triangle mark the incenter.C10 Perpendicular Bisector Concurrency: The three perpendicular bisectors of a triangle mark the circumcenter.C11 Altitude Concurrency: The three altitudes of a triangle mark the orthocenter.C12 Circumcenter: The circumcenter of a triangle is equidistant from the three vertices.C13 Incenter: The incenter of a triangle is equidistant from the three sides.C14 Median Concurrency: The three medians of a triangle mark the centroid.C15 Centroid Conjecture: The centroid of a triangle divides each median into two parts so that the distance from the centroid to the vertex is half the distance from the centroid to the opposite side.C16 Center of Gravity: The centroid of a triangle is the center of gravity the triangular region.C17 Triangle Sum: The sum of the measures of the angles in every triangle is 180 degrees.C18 Isosceles Triangle: If a triangle is isosceles, then the base angles are congruent.C19 Converse Isosceles Triangle: If a triangle has two congruent angles, then it is isosceles.C20 Triangle Inequality: The sum of the lengths of any two sides of a triangle is greater than the length of the third side.C21 Side-Angle Inequality: In a triangle, if one side is longer than the other side, then the angle opposite the longer side is the biggest angle.C22 Equiangular Triangle Exterior Angle: The measure of an exterior angle of an equilateral triangle is 120 degrees.C23 SSS Congruence: If three sides of one triangle are congruent to the three sides of another triangle, then the triangles are congruent.C24 SAS Congruence: If two sides and the included angle of one triangle are congruent to the corresponding two sides and the included angle of another triangle, then the triangles are congruent.C25 ASA Congruence: If two angles and the included side of one triangle is congruent to the corresponding two angles and the included side of another triangle, the two triangles are congruent.C26 SAA Congruence: If two angles and a non-included side of one triangle are congruent to the corresponding two angles and non-included side of another triangle, then the two triangles are congruent.C27 Vertex Angle Bisector: In an isosceles triangle, the bisector of the vertex angle is also the altitude and median.C28 Equilateral/Equiangular Triangle: Every equilateral triangle is equiangular, and every equiangular triangle is equilateral.C29 Quadrilateral Sum: The sum of the measures of the four interior angles of any quadrilateral is 360 degrees.C30 Pentagon Sum: The sum of the measures of the four interior angles of any pentagon is 540 degrees.C31 Polygon Sum: The sum of the interior angles of any polygon is n-2(180).C32 Exterior Angle Sum: For any polygon, the sum of the measures of the exterior angles will equal 360 degrees.C33 Equiangular Polygon: For any equiangular polygon, you can find the measure of one exterior angle by dividing 360 by the number of sides or subtracting the measure of an interior angle from 360.C34 Kite Angles: The vertex angles of a kite are congruent, the non vertex angles of a kite are also congruent.C35 Kite Diagonals: The diagonals of a kite are perpendicular.C36 Kite Diagonal Bisector: The diagonal connecting the vertex angles of a kite is perpendicular bisector of the other diagonal.C37 Kite Angle Bisector: The vertex angles of a kite are bisected by a diagonal.C38 Trapezoid Consecutive Angles: The consecutive angles between the bases of a trapezoid are supplementary.C39 Isosceles Trapezoid Conjecture: The base angles of a isosceles trapezoid are congruent.C40 Isosceles Trapezoid Diagonal Conjecture: The diagonals of an isosceles trapezoid are congruent.C41 Three Midsegments: The three midsegments of a triangle divides it into four congruent triangles.C42 Triangle Midsegment: A midsegment of a triangle is parallel to the third side and half the length of the third side.C43 Trapezoid Midsegment: The midsegment of a trapezoid is parallel to the bases and is equal in length to the averages of the lengths of the bases.C44 Parallelogram Opposite Angles: The opposite angles of a parallelogram are congruent.C45 Parallelogram Consecutive Angles: The consecutive angles of a parallelogram are supplementary.C46 Parallelogram Opposite Sides: The opposite sides of a parallelogram are parallel and congruent.C47 Parallelogram Diagonals: The diagonals of a parallelogram are bisected by one another.C48 Double Edged Straightedge: If two parallel lines are intersected by a second pair of parallel lines that are the same distance apart, then the parallelogram formed is a rhombus.C49 Rhombus Diagonals: The diagonals of a rhombus are perpendicular and they bisect each other.C50 Rhombus Angles: The diagonals of a rhombus bisect the angles of the rhombus.C51 Rectangle Diagonals: The diagonals of a rectangle are bisectors to each other and are congruent.C52 Square Diagonals: The diagonals of a square bisect each other, bisect the angles, and are congruent.C53 Tangent Conjecture: A tangent to a circle is perpendicular to the radius drawn to the point of tangency.C54 Tangent Segments Conjecture: Tangent segments to a circle from a point outside the circle are congruent.
If two lines intersect to form adjacent congruent angles then the lines are?
That is an important theorem in geometry: if two lines intersect to form adjacent congruent angles, then the lines are perpendicular. Those congruent angles would be right angles.
If two angles form a linear pair then they are adacent and?
congruent congruent
How can I prove an angle bisector?
It depends on what is given.In general, one half of the bisected angle is proven to congruent to the other half. By the Definition of an Angle Bisector, the bisected angle can be proven bisected.---- To show that two angles are congruent:One way to prove the two angles congruent is to show that their measures are equal. This can be done if there are numbers on the diagram. Use the Protractor Postulate or the Angle Addition Postulate to find the smaller angles' measures, if they are not directly marked. Then use the Definition of Congruent Angles to prove them congruent.Given that the smaller angles correspond on a congruent or similar pair of figures in that plane and form an angle bisector, the Corresponding Parts of Congruent Figures Postulate or Corresponding Parts of Simlar Figures Postulate may be used.
Do a bisector of an angle divides the angle into right angles?
A bisector divides an angle into two equal parts. Therefore, if the bisector begins on the middle of a straight line (180 degrees) then the bisector must form a right-angle with the straight line.
What does a perpendicular bisector of a triangle split into two congruent parts?
That will depend on what type of triangle it is as for example if it is an isosceles triangle then it will form two congruent right angle triangles.
Why vertical angles must always be congruent?
Because if they werent, they would eventually form an angle.
What is a counterexample for all intersecting lines form right angles?
Say angle 1 is 40 which means that if angle 3 is congruent then angle 3 is also 40 by definition of vertical angles. That would make angle 2 equal to 140 by definition of a linear pair and so angle 4 is congruent by vertical angles.
Which figure does a diagonal always form a angle bisector a rectangle a trapezoid a square or a quadrilateral?
A diagonal always forms an angle bisector in a square. In a rectangle, trapezoid, or any other quadrilateral, a diagonal does not always bisect the angles.
If two angles are vertical angles then they are congruent?
yes they are because they meet to form at a right angle
Which of these can not form a perpendicular bisector?
Perpendicular bisector lines intersect at right angles
What is the pair of congruent angles that form one of the bases of an isosceles trapezoid?
They are congruent angles.
Is it true a trapezoid has both pairs of opposite angle that are congruent?
No only if its in the form of an isosceles trapezoid then its base angles will be the same but opposite angles are normally different.
What is a opposite angles formed by the intersection of two lines?
If the two lines form an X then each angle directly across from another is congruent or equal to that angle.
What conjectures in Classic or Euclidean Geometry have been proved from elementary axioms?
All the below listed conjectures (first letter C of Conjecture) can be proved using the Euclidean axioms of geometry. They can be used to teach or learn geometry. In this way one "discovers" the power of the Euglidean axioms.Some may be beyond this goal as they stand, as the definitions of key concepts is not included (e.g., centroid [C15], or "vertical" angle [C2], sometimes called a "right" angle.C1 Linear Pair: If two angles form a linear pair, then they are supplementary and total 180 degrees.C2 Vertical Angles: If two angles are vertical angles (right angles), then they are congruent.C3a Corresponding Angles: If two parallel lines are cut by a transversal, then the corresponding angles are congruent.C3b Alternate Interior Angles: If two parallel lines are cut by a transversal, then alternate interior angles are congruent.C3 Parallel Lines: If two parallel lines are cut by a transversal, then corresponding angles are congruent, alternate interior angles are congruent, and alternate exterior angles are congruent.C4 Converse of Parallel Lines: If two lines are cut by a transversal to form pairs of congruent corresponding angles, congruent interior angles, or congruent exterior angles, then the lines are parallel.C5 Perpendicular Bisector: If a point is on the perpendicular bisector of a segment, then it is equidistant from the endpoint.C6 Converse of Perpendicular Bisector: If a point is equidistant from the endpoints of a segment, then it is on the perpendicular bisector of the segment.C7 Shortest Distance: The shortest distance from a point to a line is measured along the perpendicular bisector from the point to the line.C8 Angle Bisector: If a point is on the bisector of an angle, then it is equidistant from the sides of the angle.C9 Angle Bisector Concurrency: The three angle bisectors of a triangle mark the incenter.C10 Perpendicular Bisector Concurrency: The three perpendicular bisectors of a triangle mark the circumcenter.C11 Altitude Concurrency: The three altitudes of a triangle mark the orthocenter.C12 Circumcenter: The circumcenter of a triangle is equidistant from the three vertices.C13 Incenter: The incenter of a triangle is equidistant from the three sides.C14 Median Concurrency: The three medians of a triangle mark the centroid.C15 Centroid Conjecture: The centroid of a triangle divides each median into two parts so that the distance from the centroid to the vertex is half the distance from the centroid to the opposite side.C16 Center of Gravity: The centroid of a triangle is the center of gravity the triangular region.C17 Triangle Sum: The sum of the measures of the angles in every triangle is 180 degrees.C18 Isosceles Triangle: If a triangle is isosceles, then the base angles are congruent.C19 Converse Isosceles Triangle: If a triangle has two congruent angles, then it is isosceles.C20 Triangle Inequality: The sum of the lengths of any two sides of a triangle is greater than the length of the third side.C21 Side-Angle Inequality: In a triangle, if one side is longer than the other side, then the angle opposite the longer side is the biggest angle.C22 Equiangular Triangle Exterior Angle: The measure of an exterior angle of an equilateral triangle is 120 degrees.C23 SSS Congruence: If three sides of one triangle are congruent to the three sides of another triangle, then the triangles are congruent.C24 SAS Congruence: If two sides and the included angle of one triangle are congruent to the corresponding two sides and the included angle of another triangle, then the triangles are congruent.C25 ASA Congruence: If two angles and the included side of one triangle is congruent to the corresponding two angles and the included side of another triangle, the two triangles are congruent.C26 SAA Congruence: If two angles and a non-included side of one triangle are congruent to the corresponding two angles and non-included side of another triangle, then the two triangles are congruent.C27 Vertex Angle Bisector: In an isosceles triangle, the bisector of the vertex angle is also the altitude and median.C28 Equilateral/Equiangular Triangle: Every equilateral triangle is equiangular, and every equiangular triangle is equilateral.C29 Quadrilateral Sum: The sum of the measures of the four interior angles of any quadrilateral is 360 degrees.C30 Pentagon Sum: The sum of the measures of the four interior angles of any pentagon is 540 degrees.C31 Polygon Sum: The sum of the interior angles of any polygon is n-2(180).C32 Exterior Angle Sum: For any polygon, the sum of the measures of the exterior angles will equal 360 degrees.C33 Equiangular Polygon: For any equiangular polygon, you can find the measure of one exterior angle by dividing 360 by the number of sides or subtracting the measure of an interior angle from 360.C34 Kite Angles: The vertex angles of a kite are congruent, the non vertex angles of a kite are also congruent.C35 Kite Diagonals: The diagonals of a kite are perpendicular.C36 Kite Diagonal Bisector: The diagonal connecting the vertex angles of a kite is perpendicular bisector of the other diagonal.C37 Kite Angle Bisector: The vertex angles of a kite are bisected by a diagonal.C38 Trapezoid Consecutive Angles: The consecutive angles between the bases of a trapezoid are supplementary.C39 Isosceles Trapezoid Conjecture: The base angles of a isosceles trapezoid are congruent.C40 Isosceles Trapezoid Diagonal Conjecture: The diagonals of an isosceles trapezoid are congruent.C41 Three Midsegments: The three midsegments of a triangle divides it into four congruent triangles.C42 Triangle Midsegment: A midsegment of a triangle is parallel to the third side and half the length of the third side.C43 Trapezoid Midsegment: The midsegment of a trapezoid is parallel to the bases and is equal in length to the averages of the lengths of the bases.C44 Parallelogram Opposite Angles: The opposite angles of a parallelogram are congruent.C45 Parallelogram Consecutive Angles: The consecutive angles of a parallelogram are supplementary.C46 Parallelogram Opposite Sides: The opposite sides of a parallelogram are parallel and congruent.C47 Parallelogram Diagonals: The diagonals of a parallelogram are bisected by one another.C48 Double Edged Straightedge: If two parallel lines are intersected by a second pair of parallel lines that are the same distance apart, then the parallelogram formed is a rhombus.C49 Rhombus Diagonals: The diagonals of a rhombus are perpendicular and they bisect each other.C50 Rhombus Angles: The diagonals of a rhombus bisect the angles of the rhombus.C51 Rectangle Diagonals: The diagonals of a rectangle are bisectors to each other and are congruent.C52 Square Diagonals: The diagonals of a square bisect each other, bisect the angles, and are congruent.C53 Tangent Conjecture: A tangent to a circle is perpendicular to the radius drawn to the point of tangency.C54 Tangent Segments Conjecture: Tangent segments to a circle from a point outside the circle are congruent.
