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13 votes
13 votes
Are the triangles similar?

A. Yes by the AA rule
B. yes by the SSS rule
C. not similar
D. yes by the SS rule.

Are the triangles similar? A. Yes by the AA rule B. yes by the SSS rule C. not similar-example-1
User Luca Schimweg
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2 Answers

20 votes
20 votes
C. Not similar hope this helps
User Relaxing In Cyprus
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17 votes

The correct option is a.

This is because the triangles seem to have at least two angles that are congruent, which is sufficient to establish similarity by the AA rule. The SSS rule cannot be confirmed without knowing the lengths of the sides, and there's no indication of side lengths to apply the SAS rule. The SS rule is not a standard rule for triangle similarity.

To determine whether the two triangles in the image are similar, we can apply the similarity rules for triangles. These rules are:

1. Angle-Angle (AA) Similarity Postulate: If two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar.

2. Side-Side-Side (SSS) Similarity Theorem: If the corresponding sides of two triangles are proportional, then the triangles are similar.

3. Side-Angle-Side (SAS) Similarity Theorem: If two sides of one triangle are proportional to two sides of another triangle, and the included angles are congruent, then the triangles are similar.

we can attempt to identify the criteria for similarity.

Step 1: Look for congruent angles. If there are two angles in each triangle that are marked as congruent, then the triangles are similar by AA rule.

Step 2: Check if the sides of the triangles are marked with any proportional lengths or segments. If the sides of one triangle are proportional to the sides of the other triangle, then the triangles are similar by SSS rule.

Step 3: Check for a combination of proportional sides and congruent included angles. If two sides of one triangle are in proportion to two sides of another triangle and the angles between those sides are congruent, then the triangles are similar by SAS rule.

Step 4: If none of the above criteria are met, then the triangles are not similar.

In the provided Triangles, there are arc marks on the angles, which may indicate that those angles are congruent. If we assume that there are two angles in each triangle with arc marks, and those arcs represent congruent angles, then the triangles would be similar by the AA rule.

Based on the information visible and typical geometric notation, the most likely answer is Yes, by the AA rule.

User Sugendran
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