If two triangles have sides in the ratio 3:4:5, what can be said about their sim

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Question: If two triangles have sides in the ratio 3:4:5, what can be said about their similarity?

Options:

Correct Answer: They are similar

Solution:

Triangles with sides in the same ratio are similar.

If two triangles have sides in the ratio 3:4:5, what can be said about their similarity?

If two triangles have sides in the ratio 3:4:5, what can be said about their similarity?

Step 1: Understand what a ratio is. A ratio compares two or more quantities. In this case, the ratio 3:4:5 compares the lengths of the sides of the triangles.
Step 2: Recognize that the sides of the triangles are in the same ratio. This means that if one triangle has sides of lengths 3x, 4x, and 5x (where x is a positive number), the other triangle has sides of lengths 3y, 4y, and 5y (where y is also a positive number).
Step 3: Learn about triangle similarity. Two triangles are similar if their corresponding sides are in the same ratio.
Step 4: Since both triangles have sides in the ratio 3:4:5, their corresponding sides are proportional.
Step 5: Conclude that because the sides of the triangles are in the same ratio, the triangles are similar.

Triangle Similarity – Triangles are similar if their corresponding sides are in proportion.
Side Ratios – Understanding that the ratio of the lengths of the sides determines the similarity of triangles.