Warm Up Circle ONE!

Bellringer Work on Warm up sheet!

Objective: Explore Triangle Congruence

Rigid Motions What are Rigid Motions??? “Motions that preserve the size and shape of figures” Who can name some Rigid Motions that we know??? Translations Rotations Reflections

Congruent = same size, same shape All the angles are the same All the side lengths are the same

Two Congruent Triangles… If I tell you that triangle CAT is congruent to triangle DOG… what else can you conclude? Tell me everything you know! O C G A T D

Highlight! pg. 910 When you write a statement such as ABC  DEF, you are also stating which parts are congruent!!! Helpful Hint

Given: ∆PQR  ∆STW Identify all pairs of corresponding congruent parts. Angles: P  S, Q  T, R  W Sides: PQ  ST, QR  TW, PR  SW

If polygon LMNP  polygon EFGH, identify all pairs of corresponding congruent parts. Angles: L  E, M  F, N  G, P  H Sides: LM  EF, MN  FG, NP  GH, LP  EH

Let’s Look at Example A on pg. 910

Given: ∆ABC  ∆DEF Find the value of x. AB  DE AB = DE 2x – 2 = 6

Given: EFG  RST. Find the values of x, y, and z.

Remember: Rigid Motions and Congruence Based on what we have learned so far, what do you need to know in order to be able to say that these two triangles are congruent? A D C B E F

Remember: What does congruent mean? Two figures are congruent if they have all of the same side lengths and angle measures. Remember: What are tick marks? Arc Marks?

What if… What if there was a way to prove triangles are congruent without using rigid motions and without finding all of the side lengths and angles…

Straw Activity! Measure and cut three pieces from the straws: One is 2 inches long One is 4 inches long One is 5 inches long Use the pre cut string that is given to you. Thread each piece of straw together so the pieces form a triangle. Compare your triangle with your table group. Are the triangles congruent?

Reflection Questions Do you think it is possible to make two triangles that have the same side lengths but are not congruent? Why or why not? Complete the following conjecture based on your results: Two triangles are congruent if __________________________

What about quadrilaterals?

SSS (Side-Side-Side) Congruence

Example of SSS Congruence Which rigid motion???

Straw Activity Part II Measure and cut two pieces from the straws: One that is 4 inches long One that is 5 inches long Use the angle measure given to you. Place the pieces of straw on the sides of the angle Without changing the angle, use a piece of straw to create a third side for your triangle. Compare your triangle with your neighbor’s triangle. Are they congruent?

Reflection Questions Suppose you know two side lengths of a triangle and the measure of the angle between these sides. Can the length of the third side be any measure? Explain. Complete the following conjecture based on your results: Two triangles are congruent if ________________________________

An included angle is an angle formed by two adjacent sides of a polygon. B is the included angle between sides AB and BC.

SAS Congruence Caution The letters SAS are written in that order because the congruent angles must be between pairs of congruent corresponding sides. Caution

Example of SAS Congruence Which rigid motion???

Are the triangles congruent? Explain your reasoning.

A Video… https://www.khanacademy.org/math/geometry/congruence/triangle- congruence/v/more-on-why-ssa-is-not-a-postulate

SSA is not a shortcut! Write down when it is not a shortcut.

Remember: For right triangles…

HL Congruence (Special Case of SSA)

Example of HL Congruence Which rigid motion???

Homework SSS pg. 1033 (10-14) SAS pg. 1020 (2-7) Pg. 915- 916 (4-7