Big Idea: Prove Triangles are Congruent by SAS and HL

GEOMETRY 10/22/14 BELLWORK

GEOMETRY 4.4

Big Idea: Prove Triangles are Congruent by SAS

and HL

Postulate 20 Side-Angle-Side (SAS) Congruence TheoremIf two sides and the included angle of one triangle are congruent to two sides and the included angle of a second triangle, then the two triangles are congruent.

R

S

T U

V

W

If Side

Angle

Side

then

Hypotenuse

Leg

Leg

Review: Parts of a right triangle

Theorem 4.5 Hypotenuse-Leg (HL) Congruence TheoremIf the hypotenuse and leg of a right triangle are congruent to the hypotenuse and leg of a second right triangle, then the two triangles are congruent.

A

BC F

D

E

Consider a relationship involving two sides, and the angle they form, their included angle.

Any time you form an angle of the same measure with the pencils, the side formed by connecting the pencil points will have the same length. In fact, any two triangles formed in this way are congruent.

Name the included angle for the following pairs of sides. and

and

and

and

and

ADB

Examples 1 to 5

Determine whether or not the triangles are congruent. Explain your reasoning. Write a

congruence statement if they are congruent.

Example 6

Determine whether or not the triangles are congruent. Explain your reasoning. Write a

congruence statement if they are congruent.

Example 6

Use the given information to name two triangles that are congruent.

Explain your reasoning.

Geometry 10/22/14Bellwork5 min. Q & A on HW

(Finish tomorrow)Textbook: Page 243-244 Exercises: 4-12 Even, 16-22 Even