The Pythagorean Theorem and Converse: Practice Level 2 | Geometry

Level 2 · Intermediate 0 / 12 answered

Question 1 of 12

1

A right triangle has legs $4\sqrt3$ cm and $5$ cm. Find its hypotenuse exactly.

Answer choices for question 1 A $\sqrt{37}$ cm B $4\sqrt3+5$ cm C $\sqrt{73}$ cm D $73$ cm
2

A right triangle has hypotenuse $2\sqrt{34}$ m and one leg $9$ m. Find the other leg.

Answer choices for question 2 A $\sqrt{55}$ m B $\sqrt{217}$ m C $\sqrt{13}$ m D $55$ m
3

A nondegenerate triangle has positive lengths $u$ , $v$ , and $w$ . Suppose $u^2+v^2=w^2$ . What follows?

Answer choices for question 3 A The angle opposite u is right. B The triangle must be equilateral. C No conclusion follows without measuring angles. D The angle opposite the side of length w is right.
4

Classify proposed side lengths $9$ , $11$ , and $15$ units.

Answer choices for question 4 A Acute triangle B Obtuse triangle C Right triangle D No nondegenerate triangle
5

Classify proposed side lengths $6$ , $10$ , and $11$ units.

Answer choices for question 5 A Acute triangle B Obtuse triangle C Right triangle D No nondegenerate triangle
6

Which statement describes lengths $3$ , $4$ , and $7$ units?

Answer choices for question 6 A They make an obtuse triangle because 49 exceeds 25. B They make a right triangle because 3 and 4 occur in a triple. C They make a flat boundary arrangement, not a nondegenerate triangle. D They make an acute triangle because all lengths are positive.
7

A right triangle is obtained from a $7,24,25$ triangle by a scale factor of $1.5$ from original to image. What is the image hypotenuse?

Answer choices for question 7 A $26.5$ units B $37.5$ units C $36$ units D $56.25$ units
8

In right triangle $ABC$ , $C$ is right and $H$ is the altitude foot on $AB$ . Here $AH$ is $7$ units and $HB$ is $18$ units. Find $BC^2+CA^2$ .

Answer choices for question 8 A $126\text{ units}^2$ B $373\text{ units}^2$ C $25\text{ units}^2$ D $625\text{ units}^2$
9

Triangle $MNP$ is right at $M$ . Side $MN$ is named $c$ , side $MP$ is named $a$ , and side $NP$ is named $b$ . Which equation is correct?

Answer choices for question 9 A $a^2+b^2=c^2$ B $b^2+c^2=a^2$ C $a^2+c^2=b^2$ D $a+c=b$
10

A right triangle has one leg $5$ cm and hypotenuse $13$ cm. A similar triangle has hypotenuse $39$ cm. What is its other leg, corresponding to the unknown leg of the first triangle?

Answer choices for question 10 A $12$ cm B $36$ cm C $15$ cm D $108$ cm
11

In the converse proof, a constructed hypotenuse $d$ and given side $c$ satisfy $d^2=c^2$ . Why does $d=c$ follow?

Answer choices for question 11 A Every real number equals its square. B All triangles with two matching sides are congruent. C The given triangle was assumed right. D Both d and c are positive lengths.
12

Three measured side lengths round to $3$ , $4$ , and $5$ cm to the nearest centimeter. What can you conclude about an exactly right angle?

Answer choices for question 12 A A right angle is possible, but these rounded data do not prove one. B The triangle must be exactly right. C The triangle must be acute. D A triangle with these rounded measurements is impossible.