Answers 25-26 KCS16 Geometry ICTrapezoids and Kites

Figures in the Coordinate Plane Answers

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If quadrilateral PQRS is a kite, which statements must be true? Select three options

QP ≅ QR

PM ≅ MR

QR ≅ RS

∠PQR ≅ ∠PSR

∠QPS ≅ ∠QRS

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Quadrilateral J K L M is shown. A diagonal is drawn from point J to point L. Sides K L and J M are parallel. Sides J K and L M are congruent. The length of J L is 18, the length of J K is 16, and the length of J M is 40. Angle M is 45 degrees.

16 units

18 units

40 units

45 units

A kite has a perimeter of 108 feet. One of the longer sides measures 30 feet. What are the lengths of the other three sides?

24 feet, 24 feet, 30 feet

24 feet, 30 feet, 30 feet

26 feet, 26 feet, 26 feet

30 feet, 48 feet, 48 feet

Quadrilateral A B C D is shown. Sides A D and B C are parallel. Sides A B and C D are congruent. Angle A is 115 degrees.

45°

65°

115°

135°

Consider kite ABCD.

x = 2, y = 22

x = 2, y = 44

x = 5, y = 22

x = 5, y = 44

Given: JKLM is an isosceles trapezoid, KL ∥ JMProve: KM ≅ JL

definition of linear pair

definition of congruence

base angles theorem

sufficient base angles theorem

Right trapezoid WXYZ is shown.

73°

90°

107°

163°

Trapezoid A B C D is shown. Sides A B and D C are parallel. Sides A D and B C are congruent. Angle B is (3 x) degrees and angle D is (9 x) degrees.

x=15

x=20

x=45

x=60

16 units

18 units

40 units

45 units

If quadrilateral PQRS is a kite, which statements must be true? Select three options

QP ≅ QR

PM ≅ MR

QR ≅ RS

∠PQR ≅ ∠PSR

∠QPS ≅ ∠QRS

A town planner wants to build two new streets, Elm Street and Garden Road, to connect parallel streets Maple Drive and Pine Avenue.

54°

72°

108°

144°

Trapezoid A B C D is shown. Sides A B and D C are parallel. Sides A D and B C are congruent. Angle B is (3 x) degrees and angle D is (9 x) degrees.

x=15

x=20

x=45

x=60

The diagram shows quadrilateral MNPQ.

8 units

10 units

11 units

15 units

Quadrilateral A B C D is shown. Sides A D and B C are parallel. Sides A B and C D are congruent. Angle A is 115 degrees.

45°

65°

115°

135°

A kite has a perimeter of 70 centimeters. One of the shorter sides measures 16 centimeters. What are the lengths of the other three sides?

16 centimeters, 16 centimeters, and 19 centimeters

16 centimeters, 19 centimeters, and 19 centimeters

16 centimeters, 38 centimeters, and 38 centimeters

18 centimeters, 18 centimeters, and 18 centimeters

Which quadrilateral is a kite?

Quadrilateral A B C D is shown. Sides B C and C D are congruent. Sides A B and A D have different lengths.

Quadrilateral E F G H is shown. Angles E and G are congruent. Sides E F and F G are congruent. Sides G H and E H are congruent.

Quadrilateral J K L M is shown. Sides K L and J M are parallel. The lengths of J K and L M are congruent. Angles J and M are congruent.

Quadrilateral N O P Q is shown. Sides O P and N Q are parallel. Sides O N and P Q are parallel. Angles P and N are congruent.

Which quadrilateral is a trapezoid?

Quadrilateral A B C D is shown. Sides A B and D C are parallel. Sides A D and B C have different length measures. Angles A and D are right angles.

Quadrilateral E F G H is shown. Sides F E and G H are congruent. Angles E and H have different measures.

Quadrilateral J K L M is shown. Sides J K and L M are parallel. Sides K L and J M are parallel.

Quadrilateral N O P Q is shown. Sides O N and N Q are congruent. Sides O P and P Q are congruent.

A town planner wants to build two new streets, Elm Street and Garden Road, to connect parallel streets Maple Drive and Pine Avenue.

54°

72°

108°

144°

Kite K L M N is shown. The lengths of sides L M and M N are congruent. The lengths of L K and K N are congruent. Angle K is 99 degrees and angle N is 106 degrees.

49°

99°

106°

155°

The diagram shows isosceles trapezoid LMNP. It also shows how line segment NO was drawn to form parallelogram LMNO.

50°

65°

80°

130°