C 15. Given: AM = MB; AD = BC; Congruent Triangles / 151 ZMDC = Z MCD 16. Given: E23; Prove: AC = BD 23 = L4; 25 = L6 Prove: BC = ED B 7/3 4\8 F 17. A, B, C, and D are noncoplanar. A ABC, AACD, and AABD are equilateral. X and Y are midpoints of AC and AD. Z is a point on AB. What kind of triangle is AXYZ? Explain. Mixed Review Exercises 1. Write the Isosceles Triangle Theorem (Theorem 4-1) and its converse (Theorem 4-2) as a single biconditional statement. Complete each statement with the word always, sometimes, or never. 2. Two isosceles triangles with congruent bases are 3. Two isosceles triangles with congruent vertex angles are congruent. congruent. congruent. 4. Two equilateral triangles with congruent bases are Draw a diagram for each of the following. 6. a. XY bisects CD. 5. a. M is between A and B. b. XY bisects CXD. b. M is the midpoint of AB. 8. a. acute isosceles AXYZ 7. a. acute scalene AJKL b. obtuse scalene AJKL b. obtuse isosceles AXYZ 10. a. equilateral AEFG b. equiangular AEFG 9. a. right scalene ARST b. right isosceles ARST 11. Write a proof in two-column form. Given: BE = CD; BD = CE Prove: AABC is isosceles. B

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Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.