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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. Two similar solids have a scale factor of 2. What is the ratio of their volumes?

    Answer: 8:1

    Volume ratio is the cube of the scale factor: 2³ = 8.

  2. In a triangle, the angle bisector divides the opposite side into segments proportional to the:

    Answer: Adjacent sides

    The Angle Bisector Theorem states the ratio equals the ratio of the two adjacent sides.

  3. If DE is parallel to BC in triangle ABC with AD = 4, DB = 6, and AE = 6, what is EC?

    Answer: 9

    By proportionality 4/6 = 6/EC, so EC = 9.

  4. Two similar pentagons have areas 16 cm² and 81 cm². What is the ratio of their sides?

    Answer: 4:9

    Take the square root of the area ratio: √16:√81 = 4:9.

  5. Which of the following always produces similar figures?

    Answer: A dilation

    A dilation preserves shape and angles, producing a similar figure.

  6. The altitude to the hypotenuse of a right triangle creates two smaller triangles that are:

    Answer: Similar to the original and each other

    The altitude-on-hypotenuse rule makes all three triangles similar.

  7. A map uses a scale of 1 inch = 25 miles. Two cities are 3.5 inches apart. What is the actual distance?

    Answer: 87.5 miles

    Multiply 3.5 × 25 = 87.5 miles.