5.4 Proving Triangle Congruence by SSS

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Proving Triangles Congruent

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Presentation transcript:

5.4 Proving Triangle Congruence by SSS

Using the SSS Congruence Theorem

Example 1: Using the SSS Congruence Theorem Write a proof. Statements Reasons S 1. ) Given 2.) Given 3.) Reflexive Property of Congruence 4.) SSS Congruence Theorem

No, all corresponding sides are not congruent. You try! Yes, all corresponding sides are congruent, so by the SSS of Congruence Theorem the triangles are congruent. No, all corresponding sides are not congruent. Yes, all corresponding sides are congruent, so by the SSS of Congruence Theorem the triangles are congruent.

Example 2: Solving a Real-Life Problem Explain why the bench with the diagonal support is stable, while the one without the support can collapse. The bench with the diagonal supports form triangles with fixed side lengths. By the SSS Congruence Theorem, these triangles cannot change shape, so the bench is stable. The bench without the support is not stable because there are many possible quadrilaterals with the given side lengths.

You try! Determine whether the figure is stable. Explain your reasoning. Not stable. Many possible quadrilaterals with the given side lengths. Stable. The support forms triangles and by the SSS Congruence Theorem these figures cannot change shape. Not stable. Many possible quadrilaterals with the given side lengths.

Vocabulary In a right triangle the sides adjacent to the right angle are called legs. The side opposite of the right angle is called the hypotenuse.

Using the Hypotenuse-Leg Congruence Theorem

Example 3:Using the Hypotenuse-Leg Congruence Theorem Write a proof. Hint: Redraw the figure with the triangles side by side with corresponding parts in the same position. Mark the given information on the diagram. Don’t forget about the overlapping side in the original figure. What does that say about those side lengths?

Example 3 Continued Statements Reasons 1.) Given 2.) Given 3.) <Z and <Y are right angles. 3.) Definition of lines are right triangles. 4.) Definition of a right triangle 5.) Reflexive Property of Congruence 6.) HL Congruence Theorem

You Try! 8. 7.