AMSCO'S Geometry. New York - Rye High School

Proving Triangles Congruent Using Angle, Side,Angle 161Applying SkillsIn 12–14:a. Draw a diagram with geometry software or pencil and paper and write a given statementusing the information in the first sentence.b. Use the information in the second sentence to write a prove statement.c. Write a proof.12. ABC and DBE bisect each other. Prove that ABE CBD.13. ABCD is a quadrilateral; AB = CD; BC = DA; and DAB, ABC, BCD, and CDA areright angles. Prove that the diagonal AC separates the quadrilateral into two congruent triangles.14. PQR and RQS are a linear pair of angles that are congruent and PQ QS. Prove thatPQR RQS.4-6 PROVING TRIANGLES CONGRUENT USINGANGLE, SIDE, ANGLEIn the last section we saw that it is possible to prove two triangles congruent byproving that fewer than three pairs of sides and three pairs of angles are congruent,that is, by proving that two sides and the included angle of one triangleare congruent to the corresponding parts of another. There are also other waysof proving two triangles congruent.Hands-On ActivityIn this activity, we will use a protractor and ruler, or geometry software.Use the procedure below to draw a triangle given the measures of twoangles and of the included side.STEP 1. Use the protractor or geometry software todraw an angle with the first given angle measure.Call the vertex of that angle A.STEP 2. Draw a segment with the given length alongone of the rays of A. One of the endpoints ofthe segment should be A. Call the other endpointB.AAB