Congruent Triangles ABC and CDA: Finding Equal Angles

Triangles ABC and CDA are congruent.

Which angle is equal to angle BAC?

AAABBBEEECCCDDD

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Step-by-step video solution

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00:00 In overlapping triangles, which angle corresponds to angle BAC?
00:03 The triangles are overlapping according to the given information
00:09 Let's examine all corresponding angles in order
00:34 When writing an angle with 3 letters, the middle letter represents the vertex
00:46 Therefore, we'll find the corresponding angles for these triangles
00:51 And this is the solution to the question

Step-by-step written solution

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1

Understand the problem

Triangles ABC and CDA are congruent.

Which angle is equal to angle BAC?

AAABBBEEECCCDDD

2

Step-by-step solution

We observe the order of the letters in the congruent triangles and write the matches (from left to right).

ABC=CDA ABC=CDA

That is:

Angle A is equal to angle C.

Angle B is equal to angle D.

Angle C is equal to angle A.

From this, it is deduced that angle BAC (where the letter A is in the middle) is equal to angle C — that is, to angle DCA (where the letter C is in the middle).

3

Final Answer

C

Practice Quiz

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Look at the triangles in the diagram.

Which of the statements is true?

727272727272131313222131313222AAABBBCCCDDDEEEFFF

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