OBJECTIVE: 7x – 50 = 3x + 2x + 10 7x – 50 = 5x + 10 2x = 60 x = 30 Given two triangles, students will determine whether the triangles are congruent using the Side-Side-Side postulate 7x – 50 = 3x + 2x + 10 7x – 50 = 5x + 10 2x = 60 x = 30

Essential Question Learning Objective What are the shortcuts to knowing if two triangles are congruent? Given triangles, I will explain whether they are congruent or not by SSS (side-side-side).

The Idea of a Congruence Two geometric figures with exactly the same size and shape. A C B D E F

How much do you need to know. . . . . . about two triangles to prove that they are congruent?

These relationships help define the congruent triangles. In the figure, ΔABC  ΔFDE. A As in a mapping, the order of the _______ indicates the corresponding parts. vertices C B Congruent Angles Congruent Sides A  F AB  FD F E D B  D BC  DE C  E AC  FE These relationships help define the congruent triangles.

Do you need all six ? NO !

Side-Side-Side (SSS) AB  DE BC  EF AC  DF ABC   DEF B A C E D F

Triangles are congruent. Postulate 19 SSS Postulate If three _____ of one triangle are congruent to _____ _____________ sides of another triangle, then the two Triangles are congruent. sides three corresponding A B C R S T If AC  RT and AB  RS and BC  ST then ΔABC  ΔRST

Sample Answer: ΔZXY  ΔFDE In two triangles, ZY  FE, XY  DE, and XZ  DF. Write a congruence statement for the two triangles. X D Z Y F E Sample Answer: ΔZXY  ΔFDE

Pair Share Is there enough information to prove the triangles are congruent? YES NO What else is needed? All Sides  RS  TV

Yes; RTRT by the Reflexive property so ∆RST∆RQT by SSS Yes; BDDB by the Symmetric property so ∆ABD∆CDB by SSS Yes; corresponding sides are congruent so ∆ABC∆DEF by SSS

∆VWR is not a right triangle SR = 3 and RT = 5 Use the distance formula or Pythagorean Theorem to find PR and ST. ∆VWR is not a right triangle Check to see if PR  ST ST = PR = ∆PQR∆SRT by SSS HOUSTON, WE HAVE A PROBLEM!!

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You try: Why are they congruent? F D C A E B

This idea of triangles is used in engineering. Let’s see how

Exit Slips 2. 1. 3.

What Was the Objective for Today? Students will use side lengths to prove triangles are congruent. Mastery is 80% or better on 5-minute checks and practice problems.

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