26. This problem will prepare you for the Multi-Step Test Prep on page 238.
Many origami models begin with a square piece of paper,
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JKLM, that is folded along both diagonals to make the
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creases shown. JL and MK are perpendicular bisectors
of each other, and ∠NML ≅ ∠NKL.
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a. Explain how you know that KL and ML are congruent.
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b. Prove △NML ≅ △NKL.
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27. Draw a diagram and then write a proof.
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Given: BD ⊥ AC. D is the midpoint of AC. AB ≅ CB, and BD bisects ∠ABC.
Prove: △ABD ≅ △CBD
28. Critical Thinking Draw two triangles that are not congruent but have an area of
4 cm 2 each.
29.
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Given △MPQ ≅ △EDF.
Two solutions for finding m∠E are shown.
Which is incorrect? Explain the error.
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30. Write About It Given the diagram of the
triangles, is there enough information to prove
that △HKL is congruent to △YWX? Explain.
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31. Which congruence statement correctly indicates
that the two given triangles are congruent?
△ABC ≅ △EFD
△ABC ≅ △DEF
△ABC ≅ △FDE
△ABC ≅ △FED
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32. △MNP ≅ △RST. What are the values of x and y?
1
2
x = 26, y = 21_
x = 25, y = 20_
3
3
1
2
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x = 27, y = 20
x = 30 , y = 16_
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33. △ABC ≅ △XYZ. m∠A = 47.1°, and m∠C = 13.8°. Find m∠Y.
13.8
76.2
42.9
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34. △MNR ≅ △SPQ, NL = 18, SP = 33, SR = 10, RQ = 24,
and QP = 30. What is the perimeter of △MNR?
79
87
85
97
236
Chapter 4 Triangle Congruence
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