Questions: Geometry Parallelograms Quiz 4.1 REVIEW For problems 1-5, state which definition/t problem. Then solve each problem. 1. W X Y Z is a parallelogram. 2. Find m angle X. Definition/Property #: m angle X= 4. B C D E is a parallelogram. Find D B. Definition/Property #: D B=L For problems 6-8, state which definition/pr problem. Then solve each problem.

Geometry
Parallelograms
Quiz 4.1 REVIEW
For problems 1-5, state which definition/t problem. Then solve each problem.
1. W X Y Z is a parallelogram.
2. Find m angle X.

Definition/Property #:
m angle X=

4. B C D E is a parallelogram. Find D B.

Definition/Property #:
D B=L

For problems 6-8, state which definition/pr problem. Then solve each problem.

Transcript text: Geometry Parallelograms Quiz 4.1 REVIEW For problems 1-5, state which definition/t problem. Then solve each problem. 1. $W X Y Z$ is a parallelogram. 2. Find $m \angle X$. Definition/Property \#: $\qquad$ \[ m \angle X= \] 4. $B C D E$ is a parallelogram. Find $D B$. Definition/Property \#: $\qquad$ \[ D B=\underline{L} \] For problems 6-8, state which definition/pr problem. Then solve each problem.

Solution

Solution Steps

Step 1: Identify the given information

The figure WXYZ is a parallelogram, and angle Z is 105°.

Step 2: Apply the property of parallelograms

Consecutive angles in a parallelogram are supplementary, meaning they add up to 180°. Therefore, m∠W + m∠Z = 180° and m∠X + m∠Y= 180°. Opposite angles in a parallelogram are congruent. Therefore, m∠W = m∠Y and m∠X = m∠Z.

Step 3: Calculate m∠X

Since m∠X = m∠Z, and m∠Z = 105°, then m∠X = 105°.

Final Answer

m∠X = 105°

Step 1: Identify the given information

BCDE is a parallelogram and BE = 11.

Step 2: Apply the property of parallelograms

The diagonals of a parallelogram bisect each other.

Step 3: Calculate DB

Since the diagonals bisect each other, BF = FE and DF = FC. BE is a diagonal, and BE = 11. The other diagonal is DB, and it is bisected by diagonal BE, so BF+FE = BE or 2 * BF = BE, where BF = 11/2 and DB = 2 * BF. Therefore, DB=11.

Final Answer

DB = 11

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