Sure, here's a step-by-step explanation:

1. The question refers to two triangles that have two pairs of equal angles. This means that for each triangle, two of its angles are the same as two angles in the other triangle.

2. According to the Angle-Angle (AA) criterion for similarity of triangles, if two angles of one triangle are respectively equal to two angles of another triangle, then the two triangles are similar.

3. The reason behind this is that if two angles of a triangle are known, the third angle is automatically determined because the sum of the angles in a triangle is always 180 degrees.

4. Therefore, if two triangles have two pairs of equal angles, it means that all their angles are equal, pair by pair.

5. When two triangles have all their angles equal pair by pair, they are similar, regardless of whether their sides are proportional or not. This is because the angles determine the shape of the triangle, and similar triangles have the same shape, though not necessarily the same size.

6. So, two triangles with two pairs of equal angles must be similar.

Question

Sure, here's a step-by-step explanation:

1. The question refers to two triangles that have two pairs of equal angles. This means that for each triangle, two of its angles are the same as two angles in the other triangle.

2. According to the Angle-Angle (AA) criterion for similarity of triangles, if two angles of one triangle are respectively equal to two angles of another triangle, then the two triangles are similar.

3. The reason behind this is that if two angles of a triangle are known, the third angle is automatically determined because the sum of the angles in a triangle is always 180 degrees.

4. Therefore, if two triangles have two pairs of equal angles, it means that all their angles are equal, pair by pair.

5. When two triangles have all their angles equal pair by pair, they are similar, regardless of whether their sides are proportional or not. This is because the angles determine the shape of the triangle, and similar triangles have the same shape, though not necessarily the same size.

6. So, two triangles with two pairs of equal angles must be similar.

Knowee AI · Accepted Answer

Sure, here's a step-by-step explanation:

1. The question refers to two triangles that have two pairs of equal angles. This means that for each triangle, two of its angles are the same as two angles in the other triangle.

2. According to the Angle-Angle (AA) criterion for similarity of triangles, if two angles of one triangle are respectively equal to two angles of another triangle, then the two triangles are similar.

3. The reason behind this is that if two angles of a triangle are known, the third angle is automatically determined because the sum of the angles in a triangle is always 180 degrees.

4. Therefore, if two triangles have two pairs of equal angles, it means that all their angles are equal, pair by pair.

5. When two triangles have all their angles equal pair by pair, they are similar, regardless of whether their sides are proportional or not. This is because the angles determine the shape of the triangle, and similar triangles have the same shape, though not necessarily the same size.

6. So, two triangles with two pairs of equal angles must be similar.

Explain why two triangles with two pairs of equal angles must be similar.

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