Similar Right Triangle Worksheet

**Page 1**

1.

Is any triangle among the triangles in ΔABC similar to ΔDBE?

a. | No | ||

b. | Yes |

ΔABC, ΔCAD, and ΔBCD are not similar to ΔPNS as they all are right triangles

ΔDEC is also not similar to ΔDBE

[From the figure.]

Among the triangles in ΔABC no triangle is similar to ΔDBE.

Correct answer : (1)

2.

ΔABC is similar to which of the following figures?

a. | Figure 1 only | ||

b. | Figure 2 only | ||

c. | Figure 3 only | ||

d. | All the above |

ΔABC is a right triangle.

[From the figure.]

The three triangles represented by figure 1, figure 2, and figure 3 are right triangles.

[From the figure.]

As the ΔABC is a right triangle, the three triangles represented by the three figures have same shape as that of ΔABC and so they are similar to it.

Correct answer : (4)

3.

Solve for $y$. [Given $a$ = 7 and $b$ = 28.]

a. | 12 | ||

b. | 14 | ||

c. | 17 | ||

d. | 7 |

[

[Substitute.]

(

[Cross Multiply.]

[Solve for

Correct answer : (4)

4.

Solve for $v$. [Given $a$ = 2 and $b$ = 6.]

a. | 2 | ||

b. | 6 | ||

c. | 4 | ||

d. | 5 |

[

[Substitute.]

(

[Cross Multiply.]

[Solve for

Correct answer : (1)

5.

If ΔABC is a right triangle and $\stackrel{\u203e}{\mathrm{CD}}$ is altitude to the hypotenuse, then find $m$. [Given $a$ = 14 units, $b$ = 16 units.]

a. | 9.29 units | ||

b. | 8.29 units | ||

c. | 7.29 units | ||

d. | 5.29 units |

[Given.]

ΔADC ~ ΔCDB

[

[Corresponding sides of similar triangles are proportional.]

[Substitute.]

Correct answer : (4)

6.

Find the perimeter of the right triangle ABC. [Given $a$ = 8, $b$ = 10.]

a. | 25.42 units | ||

b. | 28.42 units | ||

c. | 23.42 units | ||

d. | 33.42 units |

[Given.]

ΔADC ~ ΔCDB

[

[Substitute.]

In ΔCDB, CB

[Pythagorean theorem.]

CB

[Substitute.]

In ΔABC, AB

[Pythagorean theorem.]

10

[Substitute and Simplify.]

Perimeter of ΔABC = AB + BC + AC = 10 + 8.94 + 4.48 = 23.42 units

[Substitute and Simplify.]

Correct answer : (3)

7.

Find the perimeter of the right triangle PQR. [Given $x$ = 8.6 and $y$ = 17.2.]

a. | 61.76 units | ||

b. | 71.76 units | ||

c. | 12.16 units | ||

d. | 21.06 units |

[Given.]

ΔPQR ~ ΔPRS

[Angle PQR =

[Substitute and Simplify.]

ΔPRS ~ ΔQRS

[

[Substitute.]

[Simplify.]

In ΔQRS,

[Pythagorean theorem.]

[Substitute.]

[Simplify.]

The perimeter of ΔPQR is,

[Substitute and Simplify.]

Correct answer : (1)

8.

If ΔPQR is a right triangle and $\stackrel{\u203e}{\mathrm{RS}}$ is altitude to the hypotenuse, then find the values of $r$ and $v$. [Given $a$ = 6.6 and $b$ = 11.]

a. | 10.8 units, 15.75 units | ||

b. | 9.8 units, 13.75 units | ||

c. | 8.8 units, 16.75 units | ||

d. | 8.8 units, 13.75 units |

[Given.]

In ΔPSR,

[Pythagorean theorem.]

ΔPSR ~ ΔRSQ

[

[Corresponding sides of similar triangles are proportional.]

[Substitute.]

SQ =

[Simplify.]

[Substitute.]

Correct answer : (4)

9.

If ΔPQR is a right triangle and $\stackrel{\u203e}{\mathrm{RS}}$ is the altitude to the hypotenuse, then find the values of $a$, $b$, and $c$. [Given $x$ = 4.8 and $y$ = 9.6.]

a. | 11.75 units, 8.31 units, 6.78 units | ||

b. | 8.31 units, 6.78 units, 11.75 units | ||

c. | 10.31 units, 8.78 units, 13.75 units | ||

d. | 6.78 units, 11.75 units, 8.31 units |

[Given.]

ΔPQR ~ ΔPRS

[

[Substitute and Simplify.]

ΔPRS ~ ΔRQS

[

[Substitute.]

[Simplify.]

In ΔQRS,

[Pythagorean theorem.]

[Substitute.]

[Simplify.]

Correct answer : (2)

10.

Anny is at an Ice-cream parlor where, the path RP to her house and the path RQ to her school meet at right angle. She goes into the shopping complex, which is exactly opposite to the Ice-cream parlor. Find the distance between her house and the shopping complex. [Given $a$ = 174 and $b$ = 232.]

a. | 104.40 m | ||

b. | 197.3 m | ||

c. | 217.5 m | ||

d. | 200.92 m |

[Pythagorean theorem.]

ΔPQR ~ ΔPRS

[

[Substitute and Simplify.]

Correct answer : (1)