**Problem:**Given: $ AB \parallel DC $ and $ AB = DC $**Figure Description:**The diagram shows a quadrilateral $ABCD$ where line $AB$ is parallel to line $DC$, and these lines are equal in length. **Question:**Which congruence statement(s) can be proven using the givens and the figure above?**Options:**A. $ \triangle ABC \cong \triangle DCA $ onlyB. $ \triangle BAC \cong \triangle DAC $ onlyC. $ \triangle CAB \cong \triangle ACD $ onlyD. All three of the congruence statements above can be proven.**Instructions:**Write down all key words you see in the problem as you make your choice.(Select all that apply.)- [ ] A- [ ] B- [ ] C- [ ] D**Submit and Explain** **Educational Exercise: Understanding Rotational Angles****Problem Statement:**1. *The wheel below is rotated counterclockwise about the center, point C.* [Diagram description: The diagram shows a circle divided into 10 equal sections, resembling a wheel with a central point labeled C. There are two marked points on the circle's circumference: A and B. The sections suggest equal spacing among these points.]*Objective: Determine the rotation angle needed to move point A to point B.***Question:**What is the angle of rotation that maps point A to point B?**Multiple Choice Options:**- A. 36°- B. 72°- C. 288°- D. 324°**Instructions:**- Write down all key words and calculations as you determine the correct angle of rotation.- Consider the number of equal sections in the wheel to calculate the angle between two adjacent points.**Answer Choices (Circle the correct letter):**- ○ A- ○ B- ○ C- ○ D

Name: **Problem:**Given: $ AB \parallel DC $ and $ AB = DC $**Figure De
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Description: **Problem:**Given: $ AB \parallel DC $ and $ AB = DC $**Figure Description:**The diagram shows a quadrilateral $ABCD$ where line $AB$ is parallel to line $DC$, and these lines are equal in length. **Question:**Which congruence statement(s)

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Write down all key words you see in the problem as you make your choice. 3 Given: AB||DC and AB = DC Which congruence statement(s) can be proven using the givens and the figure above? A. AABC = ADCA only B. ABAC= ADAC only C. ACAB EACD only D. All three of the congruence statements above can be proven. (Select all that apply.) A D O O O O

Write down all key words you see in the problem as you make your choice. 3 Given: AB||DC and AB = DC Which congruence statement(s) can be proven using the givens and the figure above? A. AABC = ADCA only B. ABAC= ADAC only C. ACAB EACD only D. All three of the congruence statements above can be proven. (Select all that apply.) A D O O O O

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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Concept explainers

Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.

Topic Video

Question

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**Problem:**

Given: $ AB \parallel DC $ and $ AB = DC $

**Figure Description:**

The diagram shows a quadrilateral $ABCD$ where line $AB$ is parallel to line $DC$, and these lines are equal in length.

**Question:**

Which congruence statement(s) can be proven using the givens and the figure above?

**Options:**

A. $ \triangle ABC \cong \triangle DCA $ only

B. $ \triangle BAC \cong \triangle DAC $ only

C. $ \triangle CAB \cong \triangle ACD $ only

D. All three of the congruence statements above can be proven.

**Instructions:**

Write down all key words you see in the problem as you make your choice.

(Select all that apply.)

- [ ] A
- [ ] B
- [ ] C
- [ ] D

**Submit and Explain**

**Educational Exercise: Understanding Rotational Angles**

**Problem Statement:**

1. *The wheel below is rotated counterclockwise about the center, point C.*

[Diagram description: The diagram shows a circle divided into 10 equal sections, resembling a wheel with a central point labeled C. There are two marked points on the circle's circumference: A and B. The sections suggest equal spacing among these points.]

*Objective: Determine the rotation angle needed to move point A to point B.*

**Question:**
What is the angle of rotation that maps point A to point B?

**Multiple Choice Options:**
- A. 36°
- B. 72°
- C. 288°
- D. 324°

**Instructions:**

- Write down all key words and calculations as you determine the correct angle of rotation.
- Consider the number of equal sections in the wheel to calculate the angle between two adjacent points.

**Answer Choices (Circle the correct letter):**
- ○ A
- ○ B
- ○ C
- ○ D

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