Transcript 4-4_Prove_Triangles_Congruent_by_SAS_and_HL

Warm Up
OBJECTIVE:
Given two triangles, students will determine
whether the triangles are congruent using either
the Side-Angle-Side postulate or HypotenuseLeg Theorem.
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)
No, the second statement shows different corresponding
vertices than the first statement.
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
In a triangle, the angle formed by two given sides is called the
____________
included angle of the sides.
C is the included
angle of CA and CB
C
A
A is the included
angle of AB and AC
B
B is the included
angle of BA and BC
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
5-Minute Check
ABC
BCD
ABD
BDA
DAB
CDB
Skill Develop
included angle of one triangle are
sides and the ____________
If two
________
congruent to the corresponding sides and included angle of
another triangle, then the triangles are congruent.
S
B
Postulate 20
SAS
Postulate
C
A
If AC 
RT and
then ΔABC
A 
T
R
R and
 ΔRST
AB 
RS
Quick Write
In your notes, write your response to the following:
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.
Q
D
R
P
NO!
F
D is not the included angle for DF and EF.
E
Think…ink…Share- Report Out
NO
YES
NO
We have some special Theorems
when it comes to right triangles
Pair Share- Report out
YES
YES
SAS
HL
NO
In other words, what else do we need?
RM  FB
J  D
JM  DB
OR
JR  DF
EXIT SLIPS
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.
Hint: Write a congruence statement first
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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