Geo 07 0236

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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/////ERROR ANALYSIS/////

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?
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2 x = 26, y = 21_ x = 25, y = 20_
3
3
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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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