Warm Up

Yes, the triangles are congruent by

the SAS postulate

Hint: separate the triangles

A

B

E

B

D C

Notice that “part “of B in each triangle is actually DBE, so B in the red and blue triangles are .

OBJECTIVE:Given two triangles, students will determine whether or not the triangles are congruent using the Angle-Side-Angle postulate or Angle-Angle-Side Theorem.

YES YES NO

SAS HL

4.5 Prove Triangles Congruent by AAS and ASA.

Given two triangles, students will determine whether or not the triangles are congruent using the Angle-Side-Angle postulate or Angle-Angle-Side Theorem

Mastery is 80% or better on 5-min check and Indy work.

Quiz tomorrow 4.3-4.5

ZYQ

Hint: Write a congruence statement first

ABC Congruent to DCB

5x = 3x+102x = 10 x = 5Now check your answers to make sure the corresponding sides are in fact congruent when x = 5.

Given two triangles, students will determine whether or not the triangles are congruent using the Angle-Side-Angle postulate or Angle-Angle-Side Theorem.

Why? So you can find congruent triangles in bikes, as seen in examples 23 & 24.

Mastery is 80% or better on 5-Minute checks and Practice Problems.

ASA and AASASA and AASThe side of a triangle that falls between two given angles is called the___________ of the angles.included side It is the one side common to both angles.

A B

C

AC is the includedside of A and C

CB is the includedside of C and B

AB is the includedside of A and B

You can show that two triangles are congruent by using _________ and the___________ of the triangles.

two anglesincluded side

R

S

TA

B

C

ASA and AASASA and AAS

Postulate 21

ASAPostulate

If _________ and the ___________ of one triangle are

congruent to the corresponding angles and included side of

another triangle, then the triangles are congruent.

two angles included side

If A R and AC RT and

then ΔABC ΔRST

C T

ASA and AASASA and AAS

A B

C

You can show that two triangles are congruent by using _________ and a______________.

two anglesnonincluded side

CA and CB are the nonincluded sides of A and B

R

S

TA

B

C

Theorem 4-6

AASTheorem

If _________ and a ______________ of one triangle are

congruent to the corresponding two angles and nonincluded side of another triangle, then the triangles are congruent.

two angles nonincluded side

If A R and CB TS

then ΔABC ΔRST

C T and

D

F

E

L

M

N

ΔDEF and ΔLNM have one pair of sides and one pair of angles marked toshow congruence.

What other pair of angles must be marked so that the two triangles are congruent by AAS?

However, AAS requires the nonincluded sides.

Therefore, D and L must be marked.

If F and M are marked congruent, then FE and MN would be includedsides.

1.

2.

3.

4.

Given two triangles, students will determine whether or not the triangles are congruent using the Angle-Side-Angle postulate or Angle-Angle-Side Theorem.

Why? So you can find congruent triangles in bikes, as seen in examples 23 & 24.

Mastery is 80% or better on 5-Minute checks and Practice Problems.

In your own words explain to me what you have learned in lessons 4.1-4.5.

What areas do you feel like you need more help with?

What areas do you feel confident about? How is the pace of the class for you? Too

fast? Too slow? Do you have any suggestions that would help?

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Quiz 4.3-4.5 tomorrow!!!