Similarity Proofs and Applications

≈ 25 min

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Similarity Proofs and Applications

Triangles are similar by AA, proportional sides or proportional sides with equal included angle. A proof must state angle reasons and vertex correspondence before using side ratios.

Worked reasoning

Multiply the small length by the scale factor.
$8(3/2)=12$ cm.

Key idea

Establish similarity with a valid criterion before equating corresponding side ratios.

Two similar triangles have scale factor $3/2$ from small to large. A small corresponding side is 8 cm. Find the large side.

Which statement best captures the central mathematical idea in Similarity Proofs and Applications?

Establish similarity with a valid criterion before equating corresponding side ratios.

A similar-triangle statement needs only a picture that looks proportional.

A memorised formula is valid even when its conditions are not met.

The diagram or notation replaces the need to justify each mathematical step.

When starting a problem about Similarity Proofs and Applications, which move is most reliable?

List equal angles with reasons and write the correspondence in matching order.

Round every value before identifying the mathematical structure.

Choose the longest available formula and substitute immediately.

Assume the desired conclusion and work backwards without checking equivalence.

Which statement is a misconception that must be rejected when working with Similarity Proofs and Applications?

A similar-triangle statement needs only a picture that looks proportional.

Establish similarity with a valid criterion before equating corresponding side ratios.

List equal angles with reasons and write the correspondence in matching order.

Check all ratios follow the same correspondence order.

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