Question

key points of chapter triangles and the theorems

Answer 1

Terms Centroid - The point in a triangle at which the medians of a triangle intersect.
Circumcenter - The point at which the perpendicular bisectors of a triangle intersect.
Concurrent - Intersecting at one point; lines, rays, segments, etc. are concurrent when they intersect at one point.
External Segment - The segment contained by a secant segment with an endpoint on the circle and at the fixed point outside the circle whose points all lie outside the circle (except the endpoint on the circle).
Incircle - The point in a triangle at which the angle bisectors of a triangle intersect. This point is also the center of a circle inscribed in the triangle.
Inscribed Angle - An angle whose vertex lies on a circle and whose sides are contained by secant lines.
Internal Segment - The segment contained by a secant segment whose endpoints are both on the circle.
Isosceles Trapezoid - A trapezoid with congruent legs.
Lower Base Angles - The angles in an isosceles trapezoid whose vertices are the endpoints of the longer base.
Median Of A Triangle - A segment within a triangle with one endpoint at a vertex of the triangle and the other endpoint at the midpoint of the side opposite the vertex. Every triangle has three medians.
Midsegment - A segment within a triangle whose endpoints are midpoints of the sides of the triangle. Every triangle has three midsegments.
Orthocenter - The point at which the altitudes of a triangle intersect.
Point Of Concurrency - The intersection point of concurrent lines, segments, etc.
Remote Interior Angles - The two angles of a triangle that are not adjacent to the exterior angle which is drawn by extending one of the sides.
Secant Segment - A segment with one endpoint on a circle, the other endpoint at a fixed point outside the circle, and one point of intersection with the circle, not including its endpoint Angle Pairs

• Complementary angles sum to 90 degrees.
• Supplementary angles sum to 180 degrees.
• Two angles that are both complementary to a third angle are congruent.
• Two angles that are both supplementary to a third angle are congruent.
• Vertical angles are congruent.

Special Triangles

• The base angles of an isosceles triangle are congruent.
• The legs of an isosceles triangle are congruent.
• The sides of an equilateral triangle are equal.
• The angles of an equilateral triangle are equal.
• The acute angles of a right triangle are complementary.
• The altitude to the hypotenuse of a right triangles forms two similar triangles that are also similar to the original triangle.
• The length of the median to the hypotenuse is 1/2 the length of the hypotenuse.

Triangle Angles and Sides

• The sum of the angles of a triangle is 180 degrees.
• The measure of an exterior angle of a triangle is equal to the sum of the remote interior angles.
• The measure of an exterior angle of a triangle is greater than that of either remote interior angle.
• When two angles of a triangle are equal, their opposite sides are equal, and vice versa.
• When two angles of a triangle are unequal, their opposite sides are unequal, and vice versa.
• When two sides of a triangle are unequal, the longer side is opposite the larger angle, and vice versa.
• The sum of the lengths of any two sides of a triangle is greater than the length of the third side.