Common Core Standard HSG-SRT.B.5 Questions

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Grade 10 Similar and Congruent Figures CCSS: HSG-SRT.B.5

In [math]Delta ABC[/math], [math]AC = 5 \ "units"[/math] and [math]AB = 12 \ "units"[/math]. Find [math]AD[/math]. Round the answer to one decimal place, if necessary.

0.8 units
2.1 units
10.9 units
12 units

Grade 10 Similar and Congruent Figures CCSS: HSG-SRT.B.5

A large ladder is leaning against a wall. The base of the ladder is 10 ft away from the wall and it forms a 51.3° angle with the ground. A smaller ladder is also leaning against the wall. It's base is also 10 ft away from the wall, but it forms a 38.7° angle with the ground. If the smaller ladder reaches 8 ft up the wall, how high does the larger ladder reach up the wall? Round the answer to one decimal place, if necessary.

4.5 ft
8 ft
12.5 ft
Not enough information.

Grade 9 Similar and Congruent Figures CCSS: HSG-SRT.B.5

A tree casts a shadow 8.5 ft long. A woman 5.5 ft tall casts a shadow 4 ft long. The triangle formed by the tree and its shadow is similar to the triangle formed by the woman and her shadow. How tall is the tree? Round your answer to the nearest tenth.
Tree - Medium

Grade 10 Similar and Congruent Figures CCSS: HSG-SRT.B.5

In [math]Delta ABC[/math], [math]AC = x+6 \ "units"[/math], [math]AD = x \ "units"[/math], and [math]DB = x + 28 \ "units"[/math]. What is the value of [math]x ?[/math]

[math]x=2[/math]
[math]x=-18[/math]
[math]x=9/4[/math]
[math]x = -13/2 + 1/2sqrt(193)[/math]

Grade 10 Similar and Congruent Figures CCSS: HSG-SRT.B.5

A pinhole camera is a simple camera that has a lightproof box with one tiny hole. As light enters the small hole, an inverted image of what's in front the camera appears on the opposite side of the box. Savanna has set up a pinhole camera on a flat stand, and it captures the image of a tree which is standing almost perfectly upright. If the image inside the pinhole camera's box is 1 foot tall, the width of the box is 1.5 feet, and the distance from the tree to the front side of the pinhole camera is 14 feet, how tall is the tree? Round the answer to one decimal place, if necessary.

5.7 ft
9.3 ft
18.7 ft
21 ft

Grade 10 Similar and Congruent Figures CCSS: HSG-SRT.B.5, HSG-SRT.C.8

[math]Delta ABC[/math] and [math]Delta ACD[/math] are both right triangles, where [math]ang B[/math] and [math]ang D[/math] are right angles, and [math]ang BAC ~= ang CAD[/math]. If [math]AB = 24 \ "units"[/math] and [math]AC = 25 \ "units"[/math], what is the value of [math]CD ?[/math].

Not enough information.
49 units
24 units
7 units

Grade 10 Similar and Congruent Figures CCSS: HSG-SRT.B.5

Mark and Sharon are standing side by side. Then, Mark begins walking N45°E at a speed of 1.6 m/s. Sharon starts walking at the same time, at a speed of 1.3 m/s, in the direction S60°E. If they are about 106.8 m apart after one minute, about how far apart are they after another minute of walking at the same speed and in the same direction?

184.8 m
202.8 m
213.6 m
280.8 m

Grade 10 Similar and Congruent Figures CCSS: HSG-SRT.B.5

In the figure below, quadrilateral ABED is a parallelogram. If [math]ang 1 ~= ang 2~= ang BCF ~= ang CFD[/math], [math]CF = 6 \ "units"[/math] ([math]bar{CF}[/math] is not drawn), and [math]BF = 4 \ "units"[/math], what is the perimeter of parallelogram ABED?

20 units
28 units
32 units
Not enough information.

Grade 10 Quadrilaterals CCSS: HSG-SRT.B.5

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What is the missing reason in step 3?

The sum of the angles on a straight line is 180°
[math]ang ABF[/math] and [math]ang BFE[/math] are complimentary
Right angles are congruent
[math]ang AFB ~= ang BFE[/math]

Grade 10 Similar and Congruent Figures CCSS: HSG-SRT.B.5

In the circle pictured below with center [math]O[/math], [math]bar{AD}[/math] is tangent to the circle and [math]bar{AB}[/math] is a diameter. If [math]ang ADO ~= ang CAB[/math], [math]CB = 5 \ "units"[/math] ([math]bar{CB}[/math] is not drawn), and [math]OB = 4 \ "units"[/math], what is the length of [math]bar{OD} ?[/math]

Not enough information.
[math]32/5 \ "units"[/math]
[math]8 \ "units"[/math]
[math]10 \ "units"[/math]

Grade 10 Quadrilaterals CCSS: HSG-SRT.B.5

This question is a part of a group with common instructions. View group »

What is the missing statement in step 4?

[math]m ang AFB + m ang BFE = m ang AFE[/math]
[math]90° + 90° = 180°[/math]
[math]m ang AFB + 90° = 180°[/math]
[math]90° + m ang BFE = 180°[/math]

Grade 10 Similar and Congruent Figures CCSS: HSG-SRT.B.5

In the circle pictured below point [math]O[/math] is the center, [math]bar{AB}[/math] is a diameter, and [math]bar{AD}[/math] is tangent to the circle. If [math]ang CAB ~= ang ADO[/math], [math]CB = 2x \ "units"[/math] ([math]bar{CB}[/math] is not drawn), [math]AB = 2x+4 \ "units"[/math], and [math]OD = x + 16/3 \ "units"[/math], what is the value of [math]x ?[/math]

[math]x = 16/3[/math]
[math]x = 16/9[/math]
[math]x=3[/math]
[math]x = -10/3 +2/3sqrt(34)[/math]

Grade 10 Quadrilaterals CCSS: HSG-SRT.B.5

This question is a part of a group with common instructions. View group »

What is the missing statement in step 8?

[math]ang AFB ~= ang BFE[/math]
[math]ang AFB ~= ang EDC[/math]
[math]ang BAF ~= ang EDC[/math]
[math]ang BAF ~= ang ECD[/math]

Grade 10 Similar and Congruent Figures CCSS: HSG-SRT.B.5, HSG-SRT.C.8

In the figure below, [math]Delta ABF ~= Delta ECD[/math] and [math]FBCD[/math] is a rectangle. If [math]AF = 8 \ "units"[/math], [math]AB = 17 \ "units"[/math], and [math]FE = 27 \ "units"[/math], what is the perimeter of rectangle [math]FBCD ?[/math] Round the answer to one decimal place if necessary.

100 units
107.6 units
85 units
84 units

Grade 10 Quadrilaterals CCSS: HSG-SRT.B.5

This question is a part of a group with common instructions. View group »

What is the missing reason in step 12?

If 2 parallel lines are cut by a transversal, alternate angles are supplementary
If 2 parallel lines are cut by a transversal, consecutive exterior angles are supplementary
If 2 parallel lines are cut by a transversal, alternate interior angles are congruent
If 2 parallel lines are cut by a transversal, consecutive interior angles are supplementary