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Big Idea: Prove Triangles are Congruent by SAS and HL.

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Presentation on theme: "Big Idea: Prove Triangles are Congruent by SAS and HL."— Presentation transcript:

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2 Big Idea: Prove Triangles are Congruent by SAS and HL

3 Postulate 20 Side-Angle-Side (SAS) Congruence Theorem 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. R S TU V W If Side Angle Side then

4 Hypotenuse Leg Review: Parts of a right triangle

5 Theorem 4.5 Hypotenuse-Leg (HL) Congruence Theorem If 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 BCF D E

6  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.

7 Name the included angle for the following pairs of sides.  and ADB Examples 1 to 5

8 Determine whether or not the triangles are congruent. Explain your reasoning. Write a congruence statement if they are congruent. Example 6

9 Determine whether or not the triangles are congruent. Explain your reasoning. Write a congruence statement if they are congruent. Example 6

10 Use the given information to name two triangles that are congruent. Explain your reasoning.

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12 Geometry 10/22/14  Bellwork  5 min. Q & A on HW (Finish tomorrow)  Textbook: Page 243-244 Exercises: 4-12 Even, 16-22 Even


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