Triangle Similarity Quiz Grade 10 Mathematics - Interactive Learning Platform

🔺 Triangle Similarity Quiz

Grade 10 Mathematics - Interactive Learning Platform

Key Concepts of Triangle Similarity

1. Two figures having the same shape but not necessarily the same size are called similar figures.
2. All congruent figures are similar, but the converse is not true.
3. Two polygons of the same number of sides are similar if: (i) their corresponding angles are equal and (ii) their corresponding sides are in the same ratio.

Basic Proportionality Theorem

4. If a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, then the other two sides are divided in the same ratio.
5. If a line divides any two sides of a triangle in the same ratio, then the line is parallel to the third side.

Triangle Similarity Criteria

AAA (Angle-Angle-Angle) Similarity

SSS (Side-Side-Side) Similarity

6. AAA Similarity: If corresponding angles are equal, then triangles are similar.
7. AA Similarity: If two angles of one triangle are equal to two angles of another triangle, then the triangles are similar.
8. SSS Similarity: If corresponding sides are in the same ratio, then triangles are similar.
9. SAS Similarity: If one angle is equal and the sides including these angles are proportional, then triangles are similar.

Important Points to Remember

• All circles are similar to each other
• All squares are similar to each other
• All equilateral triangles are similar to each other
• Similar figures have the same shape but may have different sizes
• The ratio of corresponding sides in similar triangles is constant

Area and Perimeter Relationships

Key Formula: If the ratio of corresponding sides is a:b, then:

• Perimeter ratio = a:b
• Area ratio = a²:b²

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