+Warm Up1. Write a congruence statement

2. List all corresponding sides and angles using the following congruence statement

+Agenda

1. Warm Up

2. Homework Check

3. 4-2, 4-3, 4-6 Triangle Congruence Figures

4. Homework

+ Practice 4-1 Homework Check: 1. <1 = 110, <2=120 2. <4=135, <3=90

3. <5=140, <6=90, <7=40, <8 = 90

4.

5.

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7.

1. FCB 2. NMD 3. GTK 4.

5. 6. 7. <Q

8. RS 9. <QRS 10. SQ 11. QR

12. <QSR

+Today’s Objective

Use triangle congruence postulates and theorems to prove that triangles are congruent.

+4-2, 4-3, 4-6 Triangle Congruence Figures

Last week we found out that if two triangles

have three congruent sides and three

congruent angles then the two triangles must

be ____________

Just like with similarity, we don’t need all six of these to prove triangles are congruent.

Review

+

If the three sides of one triangle are congruent to the three sides of another triangle, then the two triangles are congruent.

+

If two sides and the included (between) angle of one triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent.

+ Non-example of SAS:

Why can’t we use SAS to show these triangles are congruent?

+

If two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent.

+

If two angles and a non-included side of one triangle are congruent to two angles and the corresponding non-included side of another triangle, then the triangles are congruent.

+ Special Theorem for Right Triangles:

***Only true for Right Triangles***

Remember:

Hypotenuse: Longest side, always opposite the right angle.

Legs: Other 2 shorter sides (form the right angle)

+Hypotenuse – Leg (HL) Theorem

If the hypotenuse and a leg of one right triangle are congruent to the hypotenuse and leg of another right triangle, then the triangles are congruent.

+We now have the following:

SSS – side, side, side

SAS – Side, Angle (between), Side

ASA – Angle, Side (between), Angle

AAS/SAA – Angle, Angle, Side (Not between)

HL – Hypotenuse, Leg

+NEVER USE THESE!!!!!!

Or the Reverse (NEVER write a curse word on your paper!!!)

+

Which Theorem proves the Triangles are congruent?

1.

Examples

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+Class Work

Complete the work sheet for classwork!

+Homework

Finish worksheet