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Similarity & Proportionality Flashcards

7 cards from real Geometry practice questions. Tap to flip, then mark Knew It or Still Learning — missed cards come back until you master them.

Read the first 7 Similarity & Proportionality flashcards as text

  1. The geometric mean of 4 and 9 is:

    Answer: 6

    The geometric mean is √(4 × 9) = √36 = 6.

  2. If two triangles are similar by AA, which additional information is required to prove congruence?

    Answer: One pair of corresponding sides equal

    Similar triangles become congruent only when a pair of corresponding sides is equal.

  3. In a right triangle, the altitude to the hypotenuse is the geometric mean of the two:

    Answer: Hypotenuse segments

    The altitude equals the geometric mean of the two segments it creates on the hypotenuse.

  4. Two similar cones have radii 3 and 5. What is the ratio of their surface areas?

    Answer: 9:25

    Surface area ratio is the square of the linear ratio: 3²:5² = 9:25.

  5. A proportion states a/b = c/d. Cross-multiplying gives:

    Answer: ad = bc

    Cross-multiplication of a/b = c/d yields ad = bc.

  6. If a photo is enlarged so each side triples, the new area compared to the original is:

    Answer: 9 times larger

    Area scales by 3² = 9 times.

  7. Which triangles must be similar without any measurements given?

    Answer: Two equilateral triangles

    All equilateral triangles have 60° angles, making them automatically similar.