Question

match the base to the corresponding height.
base (b) | height (h)
triangle with red base labeled b and right angle | triangle with black height labeled h and right angle
triangle with red base labeled b on the leg and right angle | triangle with black height labeled h on the leg and right angle
triangle with red base labeled b on the base and right angle | triangle with black height labeled h as altitude and right angle

Explanation:

Step1: Analyze right triangle base-height

In a right triangle, the base and height are the two legs (perpendicular sides) when one leg is the base, the other is the height. For a base on a leg, the corresponding height is the other leg. For a base on the hypotenuse, the height is the altitude to the hypotenuse.

• First row (base \( b \) on a leg): The height \( h \) should be the other leg (matching the right - angled leg pair).
• Second row (base \( b \) on a leg): Similarly, the height \( h \) is the other leg.
• Third row (base \( b \) on hypotenuse): The height \( h \) is the altitude to the hypotenuse (the dashed line perpendicular to the hypotenuse).

Step2: Match each base to height

• First base (top - left, \( b \) on a leg): Matches the top - right height \( h \) (the other leg).
• Second base (middle - left, \( b \) on a leg): Matches the middle - right height \( h \) (the other leg).
• Third base (bottom - left, \( b \) on hypotenuse): Matches the bottom - right height \( h \) (the altitude to hypotenuse).

Answer:

• Top - left base \( b \) ↔ Top - right height \( h \)
• Middle - left base \( b \) ↔ Middle - right height \( h \)
• Bottom - left base \( b \) ↔ Bottom - right height \( h \)