There are three ways to classify triangles based on sides

Transcription

1 Unit 4 Notes: Triangles 4-1 Triangle ngle-sum Theorem ngle review, label each angle with the correct classification: Triangle a polygon with three sides. There are two ways to classify triangles: by angles and by sides There are four ways to classify a triangle by its angles: There are three ways to classify triangles based on sides 1

2 an triangles be named in the following ways? Yes/No, Why? cute Scalene Isosceles Right cute Equilateral Obtuse Equilateral Right Equilateral Statement Reason

3 Triangle Exterior ngle Theorem side side Remote remote exterior 2 m<3 3

4 Practice, find the measure of each variable 4

5 4-2 Triangle ongruence & Third ngle Theorem ongruent Polygons If two polygons are congruent, then their corresponding parts are congruent. The converse can be used to prove two figures are congruent. Third-ngle-Theorem If two angles of one triangle are congruent to two angles in another triangle, then the third angles in the triangles are also congruent. 5

6 M Given: is the midpoint of H T Statement Reason

7 4-3 SSS & SS ongruence Postulates Side Side Side Triangle ongruence Postulate (SSS) If all three sides of one triangle are congruent to three sides of another triangle, then the triangles are congruent. Given:, is the midpoint of 7

8 Side ngle Side Triangle ongruence Postulate (SS) If two sides and an included angle of one triangle are congruent to two sides and an included angle of another triangle, then the two triangles are congruent. Included ngle - The angle between two sides of a triangle. Given: is the midpoint of E and E 8

9 4-4 S & S onguence ngle Side ngle Triangle ongruence Postulate (S) If two consecutive angles and the included side of a triangle are congruent to two consecutive angles and the included side of another triangle, then the triangles are congruent. Given: is the midpoint of E, E E 9

10 ngle ngle Side Triangle ongruence Theorem (S) If two consecutive angles and the corresponding side of one triangle are congruent to two consecutive angles and the corresponding side of another triangle, then the triangles are congruent. *This theorem stems from the third angle theorem. Given:, 10

11 4-5 orresponding parts of congruent triangles are congruent PT orresponding parts of congruent figures / triangles are congruent PF or PT If two figures are congruent, then all corresponding parts of those Figures/Triangles are congruent. Given: The figure with,, =, and E is the midpoint of. E 11

12 4-6 ase ngle Theorem ase angle theorem for Isosceles triangles If two sides of a triangle are congruent, then the base angles are congruent. onverse to the base angle theorem for isosceles triangles If the base angles of a triangle are congruent, then the sides opposite the base angles are congruent. Isosceles vertex angle bisector theorem The bisector of a vertex angle of an isosceles triangle is perpendicular to the base of the triangle. orollaries- If a triangle is equilateral, then it is equiangular. If a triangle is equiangular, then it is equilateral. Given: E E, =, and E is the midpoint of E 12

13 4-7 Hypotenuse Leg (HL) Theorem & Leg Leg (LL) Theorem Hypotenuse Leg (HL) ongruence Theorem - If the hypotenuse and leg of one right triangle are congruent to the hypotenuse and leg of another right triangle, then the triangles are congruent. Leg Leg (LL) ongruence Theorem - If the leg and leg of one right triangle are congruent to the leg and leg of another right triangle, then the triangles are congruent. These is not used often because of the SS Postulate Given:,, and E 13