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Chapter 5: Q4 (page 182)

The diagonals of 鈻�ABCD intersecting at Z. For the following figure, tell whether the statement must be, maybe, or cannot be true.

m鈭�DAB=85鈭�andm鈭�BCD=95鈭�

Short Answer

Expert verified

The statement cannot be true.

Step by step solution

01

Step 1. Check the figure.

Consider the figure.

02

Step 2. Apply the concept of the parallelogram.

The opposite angles of a parallelogram are congruent.

03

Step 3. Step description.

Consider ABCD is a parallelogram and diagonals AB and CD intersect at Z.

From the figure, 鈭�DABand 鈭�BCDare opposite angles of a parallelogram

Since the opposite angles of a parallelogram are congruent thus the angles 鈭�DABand 鈭�BCDare congruent such that 鈭�DAB鈮�鈭�BCD.

Therefore, the statement cannot be true.

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Most popular questions from this chapter

Draw and label a diagram. List what is given and what is to be proved. Then write a two-column proof of the theorem.

Theorem 5-7.

Quadrilateral ABCD is a parallelogram. Name the principal theorem or definition that justifies the statement.

鈭�ADX鈮�鈭�CBX

In Exercise 5 quad. ABCD is a parallelogram. Find the values of x, y, and z.

Give the reason for each step in the following proof of theorem 5-6

Given: m鈭�A=m鈭�C=x;m鈭�B=m鈭�D=y

Prove: ABCD is a parallelogram.

Proof:

Draw and label a diagram. List what is given and what is to be proved. Then write a two-column proof of the theorem.

Theorem 5-4.
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