Deck 12: Congruence and Similarity With Constructions

Question 1

An equilateral triangle with sides of length 10 cm

A)No such triangle can be constructed.
B)Exactly one such triangle can be constructed.
C)Two or more such noncongruent triangles can be constructed.

Answer 1

B

Question 2

Answer 2

Question 3

Answer 3

Answers will vary. A sample correct response would be as follows.
Mark points E and F on DC such that AE and BF are perpendicular to DC.

Question 4

Question 5

answer.

Question 6

Question 7

Question 8

Question 9

A triangle with sides of length 19 cm, 9 cm, and 26 cm

A)Exactly one such triangle can be constructed.
B)No such triangle can be constructed.
C)Two or more such noncongruent triangles can be constructed.

Question 10

Question 11

Question 12

Question 13

Question 14

Question 15

A triangle with sides of length 17 cm, 28 cm, and 8 cm

A)Two or more such noncongruent triangles can be constructed.
B)No such triangle can be constructed.
C)Exactly one such triangle can be constructed.

Question 16

An isosceles triangle with two sides of length 4 cm and an apex angle of measure 74°

A)Two or more such noncongruent triangles can be constructed.
B)No such triangle can be constructed.
C)Exactly one such triangle can be constructed.

Question 17

answer.

Question 18

answer.

Question 19

Question 20

Question 21

Question 22

Question 23

What minimum information is sufficient to determine the congruency of two rhombuses?

A)None of these.
B)The measures of one angle in each rhombus must be equal.
C)The lengths of one side and the measure of one corresponding angle of each rhombus must beequal.
D)The lengths of two adjacent sides in each rhombus must be equal.

Question 24

Question 25

Question 26

What minimum information is sufficient to determine the congruency of two equilateral triangles?

A)The lengths of one side of each triangle must be equal.
B)The measures of one angle of each triangle must be equal.
C)None of these.
D)The lengths of two sides and the included angles of each triangle must be equal.

Question 27

A right triangle with legs (the sides including the right triangle)measuring a length of 33 cm and 6 cm

A)No such triangle can be constructed.
B)Two or more such noncongruent triangles can be constructed.
C)Exactly one such triangle can be constructed.

Question 28

A triangle with sides of length 5 cm and 12 cm and an angle of 102°

A)Two or more such noncongruent triangles can be constructed.
B)No such triangle can be constructed.
C)Exactly one such triangle can be constructed.

Question 29

Question 30

A triangle with angles measuring 11° and 113° and a nonincluded side of length 11 cm

A)Two or more such noncongruent triangles can be constructed.
B)No such triangle can be constructed.
C)Exactly one such triangle can be constructed.

Question 31

The radius of a circle that circumscribes a quadrilateral is the distance from the center of the circle
to any of the perpendicular bisectors.

Question 32

A triangle with sides of length 11 cm and 11 cm and a nonincluded angle of 46°

A)No such triangle can be constructed.
B)Two or more such noncongruent triangles can be constructed.
C)Exactly one such triangle can be constructed.

Question 33

A triangle with angles of 31° and 85°

A)No such triangle can be constructed.
B)Two or more such noncongruent triangles can be constructed.
C)Exactly one such triangle can be constructed.

Question 34

Question 35

Question 36

Question 37

Question 38

Provide an appropriate response.
For what kind of triangles will the perpendicular bisectors of the sides intersect on a side of the triangle?

A)right
B)none
C)obtuse
D)acute

Question 39

The perpendicular bisectors of a triangle are always concurrent.

Question 40

An isosceles triangle with sides of length 6 cm and 15 cm

A)Exactly one such triangle can be constructed.
B)No such triangle can be constructed.
C)Two or more such noncongruent triangles can be constructed.

Question 41

When is a parallelogram a rhombus?

Question 42

No square is a trapezoid.

Question 43

A quadrilateral is a if and only if its diagonals are perpendicular.

Question 44

A quadrilateral is a if and only if opposite sides are parallel or congruent.

Question 45

True or false: A rectangle is a trapezoid.

Question 46

What is a quadrilateral with diagonals that bisect each other?

Question 47

What type of figure is formed by joining the midpoints of the adjacent sides of a rhombus?

Question 48

If a rectangle is a square, it must also be a rhombus.

Question 49

What type of figure is formed by joining the midpoints of the adjacent sides of a square?

Question 50

A square has the properties of which three quadrilaterals?

Question 51

True or false: A trapezoid is a kite.

Question 52

When is a rectangle a parallelogram?

Question 53

A nearby playground has a sandbox. Erica stretches string out to show the diagonals of the
sandbox. The diagonals are perpendicular and they bisect each other. Is the sandbox a
square?

Question 54

A sector of a circle is a pie-shaped section bounded by two radii and an arc. What is a
minimal set of conditions for determining that two sectors of the same circle are congruent?

Question 55

What type of figure is formed by joining the midpoints of adjacent sides of a
parallelogram?

Question 56

What is needed to determine the congruency of two rhombuses?

Question 57

Can a parallelogram have exactly three right angles? Explain why or why not.

Question 58

The diagonals of a rectangle bisect each other.

Question 59

Is a kite a parallelogram?

Question 60

What is needed to determine the congruency of two rectangles?

Question 61

Solve.
Explain how to construct a parallelogram given two adjacent sides. If it is not possible,
explain why.

Question 62

Solve.
Draw two parallelograms such that two angles and an included side are congruent
respectively to two angles and an included side of the other parallelogram, and yet the two
parallelograms are not congruent.

Question 63

Solve.
Given two 15-cm sides and two 10-cm sides, how many quadrilaterals can be formed
with a 75° angle?

Question 64

Solve.
How many different rotational symmetries does a square have?

A)5
B)3
C)4
D)2

Question 65

What type of figure is formed by joining the midpoints of the adjacent sides of a rectangle?

Question 66

Question 67

Solve.
Explain how to construct a parallelogram with exactly three right angles. If it is not
possible, explain why.

Question 68

Solve.
Can a quadrilateral be formed given two 10-cm sides and a 75° angle that is not a
trapezoid, parallelogram, kite, or rhombus?

Question 69

The two triangles shown below are congruent.

Question 70

Question 71

Provide an appropriate response.
The two triangles shown below are congruent. The vertices corresponding to A, B, and C (in order) are .

Question 72

Solve.
Explain how to construct a line parallel to a line l using the sliding-triangle method.

Question 73

Solve.

Question 74

Question 75

Solve.
Consider the isosceles triangles ABC and PQR. If side AB is glued to side PQ, what type of
quadrilateral is formed?

Question 76

The two triangles shown below are congruent.

Question 77

Solve.
Consider the two congruent equilateral triangles ABC and PQR. If side AB is glued to side
PQ, what type of quadrilateral is formed?

Question 78

John goes to a building and stands 100 feet away. He measures the angle of elevation to
the top of the building as 37°. He also measures the angle of elevation 100 feet away from a
different building. It is the same. He concludes that the buildings are the same height. Is
he right? Explain.

Question 79

Provide an appropriate response.
The two triangles shown below are congruent. The vertices corresponding to H, I, and J (in order) are .

Question 80

Joe is building a deck. He nails a 10-foot, 2" by 8" board along the back of the house. He
intends to use two 8-foot boards for the sides out to the corner posts. Then he will use
another 10-foot board for the end. How can Joe make sure his deck is a rectangle, not a
parallelogram, without checking the angles formed at the corners?