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PRE-ALGEBRA Congruence (9-5) What are “congruent figures”? congruent figures: figures that have the same size, shape, equal sides, and equal measures (in other words, they are exactly the same) How do you indicate congruent figures, sides, and angles? An equal sign with a wave on top ( ) is used to indicate two figures, sides, or angles that are congruent. Tick marks ( | || ||| ) are usually used to indicate (show) congruent (equal) corresponding (matching) sides Angle signs ( ) are used mark congruent (equal) angles. Rule: Congruent figures are written in the order of congruent angles. In other words the first letters are equal angles, second letters are equal angles, third letters are equal angles, and so on. Example: PRE-ALGEBRA Congruence (9-5) How do you Example: If AMN ABC, name all of the corresponding (equal) parts and identify congruent find MN. parts of congruent figures? congruent angles: M B, N C, MAN BAC, NAM CAB __ __ __ __ __ __ congruent sides: MN BC, NA CA; MA BA __ __ __ Since MN BC and BC = 100 yd., then __ MN = 100 yd. Rule: You can identify congruent (equal) triangles any of the three following How can you identify congruent ways. (equal) triangles? PRE-ALGEBRA Congruence LESSON 9-5 Additional Examples In the figure, TUV WUX. a. Name the corresponding congruent angles. WUX X, T W , TUV V b. Name the corresponding congruent sides. TV WX , TU WU , VU XU c. Find the length of WX. Since WX, TV, and TV = 300 m, WX = 300 m. PRE-ALGEBRA Examples: Write a congruency statement with the reason the following triangles How do you are congruent. identify congruent parts of congruent figures? Congruence (9-5) Example: Write a congruence statement explaining why the following triangles are congruent. __ __ MN BC Since DFE SFT are vertical (opposite) angles, they are equal. __ __ EF TF DFE SFT by Side-Angle-Side (SAS). PRE-ALGEBRA Congruence LESSON 9-5 Additional Examples List the congruent corresponding parts of each pair of triangles. Write a congruence statement for the triangles. a. ACB AC ECD EC Angle Side CAB CED Angle ACB ECD by ASA. PRE-ALGEBRA Congruence LESSON 9-5 Additional Examples (continued) b. MK MKJ JK MKJ LJ LJK JK Side Angle Side LJK by SAS. PRE-ALGEBRA Congruence LESSON 9-5 Lesson Quiz Given that 1. L O JKL MNO, complete the following. 2. JK MN 3. JL MO 4. If two sides and the angle between those sides of one triangle are congruent to two sides and the angle between those sides of another triangle, why can you conclude that the two triangles are congruent? SAS PRE-ALGEBRA