The Pythagorean Theorem and Converse: Practice Level 1 | Geometry

Level 1 · Foundational 0 / 12 answered

Question 1 of 12

1

Triangle $DEF$ is right at $E$ . Which side is its hypotenuse?

Answer choices for question 1 A $DE$ B $DF$ C $EF$ D There is no hypotenuse
2

A right triangle has legs $10$ cm and $24$ cm. Find its hypotenuse.

Answer choices for question 2 A $34$ cm B $14$ cm C $676$ cm D $26$ cm
3

A right triangle has hypotenuse $15$ units and one leg $8$ units. Find the other leg exactly.

Answer choices for question 3 A $\sqrt{161}$ units B $17$ units C $7$ units D $161$ units
4

A right triangle has legs $3$ m and $7$ m. What is its exact hypotenuse?

Answer choices for question 4 A $10$ m B $\sqrt{40}$ m C $\sqrt{58}$ m D $58$ m
5

Classify the side-length set $6$ , $8$ , and $11$ units.

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

A triangle has sides $7$ , $24$ , and $25$ units. Which statement is justified?

Answer choices for question 6 A The angle opposite the 25-unit side is right. B The angle opposite the 7-unit side is right. C The triangle is obtuse because 25 is longest. D The side lengths do not form a triangle.
7

What should you conclude about proposed side lengths $2$ , $5$ , and $8$ units?

Answer choices for question 7 A They form an obtuse triangle. B They form a right triangle. C They form an acute triangle. D They cannot form a nondegenerate triangle.
8

Triangle $ABC$ is right at $B$ . Lengths $AB$ , $BC$ , and $AC$ are named $m$ , $n$ , and $t$ , respectively. Which equation applies?

Answer choices for question 8 A $m^2=n^2+t^2$ B $t=m+n$ C $t^2=m^2+n^2$ D $t^2=m^2+n$
9

Multiply every length in the triple $(5,12,13)$ by $4$ . Which set results?

Answer choices for question 9 A $(20,48,52)$ B $(20,48,51)$ C $(9,16,17)$ D $(5,12,52)$
10

The square of a right triangle's hypotenuse is $44\text{ cm}^2$ . What is the hypotenuse in simplest radical form?

Answer choices for question 10 A $22$ cm B $4\sqrt{11}$ cm C $44$ cm D $2\sqrt{11}$ cm
11

In a right triangle, why is the hypotenuse the longest side?

Answer choices for question 11 A It always lies horizontally. B Its name begins with the letter h. C It is opposite the largest angle, the right angle. D It is whichever side was labeled c.
12

In the chapter altitude notation, prior similarity gives
$a^2=cq.$
And,
$b^2=cp.$
Which expression is their sum?

Answer choices for question 12 A $c(pq)$ B $c(p+q)$ C $c^2(p+q)$ D $p^2+q^2$