## Geometry Worksheet: Analyzing a Parallelogram### DiagramThe image shows a parallelogram labeled ABCD with a diagonal AD and a diagonal BE intersecting at point E.### InstructionsABCD is a parallelogram. Fill in the blanks.### Problems1. **$\angle ADC$ and $\angle DCB$ are _______ angles.** - Answer: _______ 2. **If $AC = 14$, then $EC =$ ______.** - Answer: _______ 3. **If $DC = x + 12$ and $AB = 2x - 4$, then the length of $DC =$ ______.** - Answer: _______ 4. **If $m\angle DAB = 106^\circ$, then $m\angle ABC =$ ______.** - Answer: _______ 5. **If $DE = 32$, then $BD =$ ______.** - Answer: _______ 6. **If $m\angle DAC = 52^\circ$, then $m\angle BCA =$ ______.** - Answer: _______ 7. **If $DA = 32$ and $CB = \frac{x}{2}$, then $x =$ ______.** - Answer: _______ 8. **If $m\angle ADB = 13$ and $m\angle CDB = 74$, then $m\angle ADC =$ ______.** - Answer: _______**Notes:** - The parallelogram ABCD is oriented with vertices labeled counterclockwise starting from A.- Diagonal AD connects points A and D.- Diagonal BE intersects diagonal AD at point E.Ensure that you evaluate corresponding angles, segment lengths, and use properties of parallelograms such as the opposite angles being equal and diagonals bisecting each other for finding the correct values.

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Answered: C. ABCD is a parallelogram. Fill in the…

C. ABCD is a parallelogram. Fill in the blanks. 1ZADC end ZDCB are angles. 2. If AC= 14, then EC D 3. If DC = x+ 12 and AB = 2x-4, then the length of DC =

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

ChapterP: Preliminary Concepts

SectionP.CT: Test

Problem 1CT

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Question

## Geometry Worksheet: Analyzing a Parallelogram

### Diagram
The image shows a parallelogram labeled ABCD with a diagonal AD and a diagonal BE intersecting at point E.

### Instructions
ABCD is a parallelogram. Fill in the blanks.

### Problems
1. **$\angle ADC$ and $\angle DCB$ are _______ angles.**
- Answer: _______

2. **If $AC = 14$, then $EC =$ ______.**
- Answer: _______

3. **If $DC = x + 12$ and $AB = 2x - 4$, then the length of $DC =$ ______.**
- Answer: _______

4. **If $m\angle DAB = 106^\circ$, then $m\angle ABC =$ ______.**
- Answer: _______

5. **If $DE = 32$, then $BD =$ ______.**
- Answer: _______

6. **If $m\angle DAC = 52^\circ$, then $m\angle BCA =$ ______.**
- Answer: _______

7. **If $DA = 32$ and $CB = \frac{x}{2}$, then $x =$ ______.**
- Answer: _______

8. **If $m\angle ADB = 13$ and $m\angle CDB = 74$, then $m\angle ADC =$ ______.**
- Answer: _______

**Notes:**
- The parallelogram ABCD is oriented with vertices labeled counterclockwise starting from A.
- Diagonal AD connects points A and D.
- Diagonal BE intersects diagonal AD at point E.

Ensure that you evaluate corresponding angles, segment lengths, and use properties of parallelograms such as the opposite angles being equal and diagonals bisecting each other for finding the correct values.

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