Write a statement that indicates that the triangles in each pair are congruent. **Title: Congruent Triangles: Identifying Congruent Pairs****Objective:** To identify a statement that indicates the congruence of two triangles in a given geometric figure.**Instruction:** Below is a geometric diagram consisting of a quadrilateral with various marked sides and angles. Your task is to select the correct pair of congruent triangles from the given options.### Diagram Explanation:The given diagram is a quadrilateral $AFBC$ with a diagonal from point $A$ to point $B$. Multiple key features and points are marked for clarity:- Points: $A$, $F$, $C$, $B$- Equal segments are indicated by tick marks on the sides and angles.### Problem Statement:Write a statement that indicates that the triangles in each pair are congruent.#### Diagram:``` A-------------C \ / \ / \ / \ / \ / \ / B / \ / \ / \ / \ / \ / \ F-------------B```*Note: Each side marked with tick marks indicates that they are equal in length.*#### Options:A) $ \triangle BAC \cong \triangle ABF $B) $ \triangle BAC \cong \triangle BF4 $C) $ \triangle BAC \cong \triangle FBA $D) $ \triangle BCA \cong \triangle FAB $#### Answer Choices:- **Option A:** $ \text{Triangle } BAC \cong \text{Triangle } ABF $- **Option B:** $ \text{Triangle } BAC \cong \text{Triangle } BF4 $- **Option C:** $ \text{Triangle } BAC \cong \text{Triangle } FBA $- **Option D:** $ \text{Triangle } BCA \cong \text{Triangle } FAB $**Decision Making:**Carefully analyze the given quadrilateral and the marked sides and angles. Select the correct option that demonstrates the congruence of triangles.**Solving Strategy:** 1. Identify pairs of triangles within the quadrilateral.2. Use the given tick marks to determine which sides and angles are equal.3. Apply the properties of congruence (Side-Side-Side, Angle-Side-A

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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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Write a statement that indicates that the triangles in each pair are congruent.

**Title: Congruent Triangles: Identifying Congruent Pairs**

**Objective:** To identify a statement that indicates the congruence of two triangles in a given geometric figure.

**Instruction:** Below is a geometric diagram consisting of a quadrilateral with various marked sides and angles. Your task is to select the correct pair of congruent triangles from the given options.

### Diagram Explanation:
The given diagram is a quadrilateral $AFBC$ with a diagonal from point $A$ to point $B$. Multiple key features and points are marked for clarity:
- Points: $A$, $F$, $C$, $B$
- Equal segments are indicated by tick marks on the sides and angles.

### Problem Statement:
Write a statement that indicates that the triangles in each pair are congruent.

#### Diagram:
```
A-------------C
\ /
\ /
\ /
\ /
\ /
\ /
B
/ \
/ \
/ \
/ \
/ \
/ \
F-------------B
```
*Note: Each side marked with tick marks indicates that they are equal in length.*

#### Options:
A) $ \triangle BAC \cong \triangle ABF $

B) $ \triangle BAC \cong \triangle BF4 $

C) $ \triangle BAC \cong \triangle FBA $

D) $ \triangle BCA \cong \triangle FAB $

#### Answer Choices:
- **Option A:** $ \text{Triangle } BAC \cong \text{Triangle } ABF $
- **Option B:** $ \text{Triangle } BAC \cong \text{Triangle } BF4 $
- **Option C:** $ \text{Triangle } BAC \cong \text{Triangle } FBA $
- **Option D:** $ \text{Triangle } BCA \cong \text{Triangle } FAB $

**Decision Making:**
Carefully analyze the given quadrilateral and the marked sides and angles. Select the correct option that demonstrates the congruence of triangles.

**Solving Strategy:**
1. Identify pairs of triangles within the quadrilateral.
2. Use the given tick marks to determine which sides and angles are equal.
3. Apply the properties of congruence (Side-Side-Side, Angle-Side-A

Polygon with three sides, three angles, and three vertices. Based on the properties of each side, the types of triangles are scalene (triangle with three three different lengths and three different angles), isosceles (angle with two equal sides and two equal angles), and equilateral (three equal sides and three angles of 60°). The types of angles are acute (less than 90°); obtuse (greater than 90°); and right (90°).

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Write a statement that indicates that the triangles in each pair are congruent. 4) B A) ABAC = AABF B) ABAC = ABFA C) ABAC = AFBA D) ABCA = AFAB A