Warm Up 1.) Find the measure of the exterior angle.

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Presentation transcript:

Warm Up 1.) Find the measure of the exterior angle. 760 (5x – 2)0 2.) Find the values of x and y given B E 420 (5x + 2)0 D A 870 3y0 C F

Prove Triangles Congruent Using SSS, SAS, HL Geometry Sections 4.4 & 4.5 Prove Triangles Congruent Using SSS, SAS, HL Objective: SWBAT use sides and angles of triangles to prove congruence.

Side Names of Triangles Right Triangles: side across from right angle is the hypotenuse, the remaining two are legs. All other triangles: All sides are called legs. leg hypotenuse leg leg leg leg

Proving Triangles Congruent Using SSS, SAS, HL Two triangles are congruent when all three angles are marked congruent and all three sides are marked congruent. There are other ways to prove two triangles are congruent. We will discuss three ways today. Once two triangles have been proven congruent to each other, then you know all the corresponding sides and angles are also congruent.

Postulate 19 Side-Side-Side (SSS) Congruence Postulate: If three sides of one triangle are congruent to three sides of a second triangle, then the two triangles are congruent. Example: because of SSS. A D B C E F

Postulate 20 Side-Angle-Side (SAS) Congruence Postulate: If 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. ** included angle is the angle in-between the two sides** Example: because of SAS. P L Q R M N

Theorem 4.5 Hypotenuse- Leg (HL) Congruence Theorem: If the hypotenuse and a leg of a right triangle are congruent to the hypotenuse and leg of a second right triangle, then the two triangles are congruent. Example: because of HL. A X B C Y Z

Does not make triangles congruent. ASS does not make triangles congruent.

Determine if the triangles are congruent and explain using SSS, SAS, or HL. 1. 2. 4. 3.

Determine if the triangles are congruent and explain using SSS, SAS, or HL. 5. 6. 7. 8.

Write a Proof

Homework Page 234-235 # 5, 7, 18, 24, 26 Page 241 -242 # 10, 12, 20, 22