The symbol = means “is equal to,” while the symbol  means “is congruent to.” The symbol = can be used to state that the measures of two objects are equal. The symbol  can be used to state that two objects are congruent (like twins) Warm Up No, the second statement shows different corresponding vertices than the first statement. OBJECTIVE: Given two triangles, students will determine whether the triangles are congruent using either the Side-Angle-Side postulate or Hypotenuse- Leg Theorem.

3 sets of  sides Students will apply Sides and Angles to prove triangles congruent by SAS or HL. Why? So you can show triangles are congruent, as seen in Ex. 33. Mastery is 80% or better on 5-minute checks and practice problems.

leg hypotenuse

In a triangle, the angle formed by two given sides is called the ____________ of the sides. included angle A B C  A is the included angle of AB and AC  B is the included angle of BA and BC  C is the included angle of CA and CB Using the SSS Postulate, you can show that two triangles are congruent if their corresponding sides are congruent. You can also show their congruence by using two sides and the ____________. included angle

 ABC  BCD  BDA  DAB  ABD  CDB 5-Minute Check

Postulate 20 SAS Postulate If ________ and the ____________ of one triangle are congruent to the corresponding sides and included angle of another triangle, then the triangles are congruent. two sides included angle A B C R S T If AC  RT and  A   R and AB  RS then ΔABC  ΔRST Skill Develop

Determine whether the triangles are congruent by SAS.  If so, write a statement of congruence and tell why they are congruent.  If not, explain your reasoning. In your notes, write your response to the following: P R Q F E D NO!  D is not the included angle for DF and EF. Quick Write

NOYE S NO Think…ink…Share- Report Out

We have some special Theorems when it comes to right triangles

YE S NO SASHL Pair Share- Report out

In other words, what else do we need? RM  FB J  DJ  D JR  DFJM  DB OR

EXIT SLIPS Hint: Write a congruence statement first On a half sheet of paper, copy the figure and solve the problem. This WILL be turned in. You may work with a partner. I am limited on what I can tell you here. Use what you have learned the last two days about congruent triangles.

What was the objective today? Students will use sides and angles to prove triangles congruent by SAS or HL. Mastery is 80% or better on 5-minute checks and practice problems.

Homework Page 243 #1-24 all