Whether the pair of triangles is congruent or not.

Question

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Answer 1

Question

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°).

Chapter A, Problem 1E

To determine

Whether the pair of triangles is congruent or not.

Expert Solution & Answer

Answer to Problem 1E

Solution:

The given pair of triangle is congruent by ASA.

Explanation of Solution

Given:

The given pair of triangle is,

Algebra and Trigonometry (MindTap Course List), Chapter A, Problem 1E

Figure (1)

Approach:

The congruence principle used is,

Angle-Side-Angle (ASA): If two angles and the included side in one triangle are congruent to the corresponding angles and side in another triangle, then the triangles are congruent.

Calculation:

The given pair of triangle is congruent by ASA principle of congruency.

If two angles and the included side in one triangle are congruent to the corresponding angles and side in another triangle, then the triangles are congruent.

Conclusion:

Hence, the given pair of triangle is congruent by ASA.

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Answer 2

Question

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°).

Chapter A, Problem 1E

To determine

Whether the pair of triangles is congruent or not.

Expert Solution & Answer

Answer to Problem 1E

Solution:

The given pair of triangle is congruent by ASA.

Explanation of Solution

Given:

The given pair of triangle is,

Algebra and Trigonometry (MindTap Course List), Chapter A, Problem 1E

Figure (1)

Approach:

The congruence principle used is,

Angle-Side-Angle (ASA): If two angles and the included side in one triangle are congruent to the corresponding angles and side in another triangle, then the triangles are congruent.

Calculation:

The given pair of triangle is congruent by ASA principle of congruency.

If two angles and the included side in one triangle are congruent to the corresponding angles and side in another triangle, then the triangles are congruent.

Conclusion:

Hence, the given pair of triangle is congruent by ASA.

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Answer 3

Question

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°).

Chapter A, Problem 1E

To determine

Whether the pair of triangles is congruent or not.

Expert Solution & Answer

Answer to Problem 1E

Solution:

The given pair of triangle is congruent by ASA.

Explanation of Solution

Given:

The given pair of triangle is,

Algebra and Trigonometry (MindTap Course List), Chapter A, Problem 1E

Figure (1)

Approach:

The congruence principle used is,

Angle-Side-Angle (ASA): If two angles and the included side in one triangle are congruent to the corresponding angles and side in another triangle, then the triangles are congruent.

Calculation:

The given pair of triangle is congruent by ASA principle of congruency.

If two angles and the included side in one triangle are congruent to the corresponding angles and side in another triangle, then the triangles are congruent.

Conclusion:

Hence, the given pair of triangle is congruent by ASA.

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Answer 4

Question

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°).

Chapter A, Problem 1E

To determine

Whether the pair of triangles is congruent or not.

Expert Solution & Answer

Answer to Problem 1E

Solution:

The given pair of triangle is congruent by ASA.

Explanation of Solution

Given:

The given pair of triangle is,

Algebra and Trigonometry (MindTap Course List), Chapter A, Problem 1E

Figure (1)

Approach:

The congruence principle used is,

Angle-Side-Angle (ASA): If two angles and the included side in one triangle are congruent to the corresponding angles and side in another triangle, then the triangles are congruent.

Calculation:

The given pair of triangle is congruent by ASA principle of congruency.

If two angles and the included side in one triangle are congruent to the corresponding angles and side in another triangle, then the triangles are congruent.

Conclusion:

Hence, the given pair of triangle is congruent by ASA.

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Answer 5

Chapter A, Problem 1E

To determine

Whether the pair of triangles is congruent or not.

Expert Solution & Answer

Answer to Problem 1E

Solution:

The given pair of triangle is congruent by ASA.

Explanation of Solution

Given:

The given pair of triangle is,

Algebra and Trigonometry (MindTap Course List), Chapter A, Problem 1E

Figure (1)

Approach:

The congruence principle used is,

Angle-Side-Angle (ASA): If two angles and the included side in one triangle are congruent to the corresponding angles and side in another triangle, then the triangles are congruent.

Calculation:

The given pair of triangle is congruent by ASA principle of congruency.

If two angles and the included side in one triangle are congruent to the corresponding angles and side in another triangle, then the triangles are congruent.

Conclusion:

Hence, the given pair of triangle is congruent by ASA.

Answer 6

Chapter A, Problem 1E

To determine

Whether the pair of triangles is congruent or not.

Expert Solution & Answer

Answer to Problem 1E

Solution:

The given pair of triangle is congruent by ASA.

Explanation of Solution

Given:

The given pair of triangle is,

Algebra and Trigonometry (MindTap Course List), Chapter A, Problem 1E

Figure (1)

Approach:

The congruence principle used is,

Angle-Side-Angle (ASA): If two angles and the included side in one triangle are congruent to the corresponding angles and side in another triangle, then the triangles are congruent.

Calculation:

The given pair of triangle is congruent by ASA principle of congruency.

If two angles and the included side in one triangle are congruent to the corresponding angles and side in another triangle, then the triangles are congruent.

Conclusion:

Hence, the given pair of triangle is congruent by ASA.

Answer 7

Chapter A, Problem 1E

To determine

Whether the pair of triangles is congruent or not.

Answer 8

Expert Solution & Answer

Answer to Problem 1E

Solution:

The given pair of triangle is congruent by ASA.

Answer 9

Expert Solution & Answer

Answer 10

Expert Solution & Answer

Answer 11

Explanation of Solution

Given:

The given pair of triangle is,

Algebra and Trigonometry (MindTap Course List), Chapter A, Problem 1E

Figure (1)

Approach:

The congruence principle used is,

Angle-Side-Angle (ASA): If two angles and the included side in one triangle are congruent to the corresponding angles and side in another triangle, then the triangles are congruent.

Calculation:

The given pair of triangle is congruent by ASA principle of congruency.

If two angles and the included side in one triangle are congruent to the corresponding angles and side in another triangle, then the triangles are congruent.

Conclusion:

Hence, the given pair of triangle is congruent by ASA.