the symbol = means “is equal to,” while the symbol means “is congruent to.” the symbol =...

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

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 includedangle of AB and AC

B is the includedangle of BA and BC

C is the includedangle of CA and CB

Using the SSS Postulate, you can show that two triangles are congruent if theircorresponding sides are congruent. You can also show their congruenceby using two sides and the ____________.included angle

ABC BCD

BDA

DAB

ABD

CDB

5-Minute Check

Postulate 20

SASPostulate

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

NO YES NO

Think…ink…Share- Report Out

We have some special Theorems when it comes to right triangles

YES YES NO

SAS HL

Pair Share- Report out

In other words, what else do we need?

RM FB

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

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