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What does a perpendicular bisector cut of a triangle into two congruent parts?
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∙ 13y ago
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Wiki User
∙ 13y ago
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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.
How can you prove a triangle ABC is isosceles if angle BAD is congruent to angle CAD and line AD is perpendicular to line Bc?
Given: AD perpendicular to BC; angle BAD congruent to CAD Prove: ABC is isosceles Plan: Principle a.s.a Proof: 1. angle BAD congruent to angle CAD (given) 2. Since AD is perpendicular to BC, then the angle BDA is congruent to the angle CDA (all right angles are congruent). 3. AD is congruent to AD (reflexive property) 4. triangle BAD congruent to triangle CAD (principle a.s.a) 5. AB is congruent to AC (corresponding parts of congruent triangles are congruent) 6. triangle ABC is isosceles (it has two congruent sides)
What Angle bisector of a triangle?
An angle is formed by two rays with a common endpoint. The angle bisector is a ray or line segment that bisects the angle, creating two congruent angles. To construct an angle bisector you need a compass and straightedge. Bisectors are very important in identifying corresponding parts of similar triangles and in solving proofs.
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.
What are the three secondary parts of a triangle?
The three secondary parts of a triangle are typically associated with one word. They are commonly called the perpendicular bisectors of the triangle.
A perpendicular bisector of a triangle splits what into two congruent parts?
It splits one side of the triangle into two congruent parts.
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.
What splits a perpendicular bisector into two congruent parts?
A perpendicular bisector splits a line segment into two congruent parts.
What are the similarities between angle bisector and perpendicular bisector?
Similarities between angle bisector and perpendicular bisector: Perpendicular bisector bisects a line segment into two equal parts at 90°. Angle bisector bisects an creating two congruent angles they both bisect into equal parts! =)
What is a perpendicular bisector on a triangle?
It is a perpendicular line (a vertical line) that divides the triangle into two equal parts.
A(n) of a triangle splits an angle of the triangle into two congruent parts?
angle bisector
What splits an angle of the triangle into two congruent parts?
An angle bisector.
What of a triangle can split an angle of the triangle into two congruent parts?
a perpendicular line.
Divides into two congruent parts?
A bisector.
To cut into two congruent parts?
bisector
What is a line that divides somthing into two congruent parts?
A bisector.A bisector.A bisector.A bisector.
A ray that divides an angle into two congruent parts?
The answer is angle bisector.
