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How many exterior angles can be drawn at one vertex of a triangle?
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∙ 12y ago
Two
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∙ 12y ago
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Do octagons have only obtuse angles?
No, not if it is a randomly-drawn 8-vertex shape. Octagons only have all- obtuse angles if it is a regular octagon, like the shape of a stop sign.
How many median are in a triangle?
Median is the line drawn from the vertex to the mid point of the opposite side. Hence there are three medians possible.
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 shape has three sides and all right angles?
A Triangle drawn accross a sphere; NOT on a plane surface.
How many diagonals can you drawn from one vertex in a 35 sided polygon?
A diagonal of a polygon is a segment drawn from one vertex to another non-adjacent vertex in a polygon. This leaves 32 diagonals that can be drawn from one vertex in a 35 sided polygon.
How many exterior angles can be drawn in a triangle?
3 and they add up to 360 degrees
What is the number of diagonals drawn from one vertex on a triangle?
The number of Diagonals in one vertex of a Triangle is 0 (zero)..
In an isosceles triangle does the median to the base bisect the vertex angle?
In the diagram, ABC is an isoscels triangle with the congruent sides and , and is the median drawn to the base . We know that ∠A ≅ ∠C, because the base angles of an isosceles triangle are congruent; we also know that ≅ , by definition of an isosceles triangle. A median of a triangle is a line segment drawn from a vertex to the midpoint of the opposite side. That means ≅ . This proves that ΔABD ≅ ΔCBD. Since corresponding parts of congruent triangles are congruent, that means ∠ABD≅ ∠CBD. Since the median is the common side of these adjacent angles, in fact bisects the vertex angle of the isosceles triangle.
Does a median of a triangle contain the midpoint of the side to which it is drawn?
Yes, the median of a triangle is from a vertex to the midpoint of the side opposite the vertex.
A median of a triangle is a line or segment that passes through a vertex and the side opposite that vertex?
A median of a triangle is a line or segment that passes through a vertex and the midpoint of the side opposite that vertex. The median only bisects the vertex angle from which it is drawn when it is an isosceles triangle.
When a circle is drawn through each vertex of a right triangle the triangle's hypotenuse will be equal to?
Its diameter.
What is a ray that is drawn through the vertex of an angle and divides into two congruent angles?
An angle bisector.
What is the measure of the vertex angle of an isosceles triangle if one of its base angles measures 70 degrees and its congruent sides each measure 15 cm?
When finding the angles, the length of the sides is irrelevant in this case.Let the triangle be ABC with ∠A the vertex and BC the base; the real question is whether you have the isosceles triangle "drawn" and labelled with the equal sides:either side of the "vertex" making the equal angles ∠B and ∠CThe equal sides are AB and AC; the base being the odd length means the angles at each end of it are the same, thus: vertex_angle = 180o - 2 x 70o= 40othe base and one side to the vertex equal (say sides AB and BC) and the other side different (AC) making the equal angles ∠A and ∠C70o angle is between the sides of equal length (∠B):The vertex is one of the two equal angles: vertex_angle = (180o - 70o) ÷ 2= 55o70o angle is between the odd side and the base (∠C):The vertex angle (∠A) is the same as the given angle (∠C), that is 70o Isosceles triangles are often drawn in the first case, but it is not necessarily so!
Is an altitude ever outside a triangle?
Sure. If one of the base angles is more than 90 degrees, then the altitude (height) is outside the triangle. Yes. This only occurs with an obtuse triangle. Because an altitude is a line drawn from a vertex to the opposite side and is perpendicular with that opposite side, it can only occur if it is outside the triangle. Look at the triangle in related links. If you look at the vertex on the top, the only way to draw the altitude would be to draw outside the triangle.
What angles can be drawn a triangle?
All triangles have 3 interior angles that add up to 180 degrees
Are the medians of a triangle equidistant from each vertex?
Every triangle has three medians, just like it has three altitudes, angle bisectors, and perpendicular bisectors. The medians of a triangle are the segments drawn from the vertices to the midpoints of the opposite sides. The point of intersection of all three medians is called the centroid of the triangle. The centroid of a triangle is twice as far from a given vertex than it is from the midpoint to which the median from that vertex goes. For example, if a median is drawn from vertex A to midpoint M through centroid C, the length of AC is twice the length of CM. The centroid is 2/3 of the way from a given vertex to the opposite midpoint. The centroid is always on the interior of the triangle.
What are the characteristics of orthocenter?
The orthocenter of a triangle is the point where the altitudes of the triangle intersect. It may lie inside, outside, or on the triangle depending on the type of triangle. In an acute triangle, the orthocenter lies inside the triangle; in a right triangle, it is at the vertex opposite the right angle; and in an obtuse triangle, it is outside the triangle.
