Congruence and Similarity Worksheet

**Page 1**

1.

A regular hexagon measures 9 cm on each side. A similar hexagon is formed by halving the side length of the original one. What will happen to perimeter of the new hexagon?

a. | perimeter does not change | ||

b. | perimeter doubles | ||

c. | perimeter halves | ||

d. | perimeter triples |

Correct answer : (3)

2.

Identify the figures that are similar but not congruent.

a. | Figure 1 and Figure 4 | ||

b. | Figure 2 and Figure 3 | ||

c. | Figure 1 and Figure 3 | ||

d. | Figure 1 and Figure 2 |

Correct answer : (3)

3.

Which of the following conditions is true for similar triangles?

a. | A pair of triangles have one equal side as well as one equal angle. | ||

b. | A pair of triangles have only one proportional side. | ||

c. | A pair of triangles have three equal angles and proportional sides. | ||

d. | A pair of triangles have two proportional angles. |

Correct answer : (3)

4.

Which of the following conditions is always true for congruent triangles?

a. | A pair of triangles have equal sides. | ||

b. | A pair of triangles have two proportional angles. | ||

c. | A pair of triangles have an equal angle and two equal sides. | ||

d. | A pair of triangles have equal hypotenuses as well as an equal angle. |

Correct answer : (1)

5.

Find the length of missing side in the similar triangles shown.

a. | 7 m | ||

b. | 10 m | ||

c. | 9 m | ||

d. | 5 m |

Correct answer : (1)

6.

Find the length of the missing side in the similar figures shown.

a. | 21 cm | ||

b. | 27 cm | ||

c. | 20 cm | ||

d. | 18 cm |

Correct answer : (1)

7.

Which of the statements is true for the figure?

a. | The triangles ABC and PQR are similar. | ||

b. | enough information is not given | ||

c. | The triangles ABC and PQR are neither similar nor congruent. | ||

d. | The triangles ABC and PQR are congruent. |

Correct answer : (4)

8.

ΔMNO and ΔSTR are congruent triangles. Find the measure of $\angle $O.

a. | 58° | ||

b. | 46° | ||

c. | 56° | ||

d. | 76° |

Correct answer : (2)

9.

The two triangles shown are similar. Find the missing side length.

a. | 60 ft | ||

b. | 50 ft | ||

c. | 55 ft | ||

d. | 72 ft |

Correct answer : (1)

10.

The quadrilateral PQRS shown is similar to quadrilateral ABCD. Find the length of AB.

a. | 21 in. | ||

b. | 25 in. | ||

c. | 30 in. | ||

d. | 27 in. |

Correct answer : (1)