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Tenth Grade (Grade 10) Similar and Congruent Figures Questions

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Grade 10 Similar and Congruent Figures CCSS: HSG-SRT.A.2

Are these two triangles similar?
Triangle ABC:

$ang A=28°, ang B=91°$
Triangle DEF:

$ang D=28°, ang E=61°$

Yes, the triangles are similar.
No, the triangles are not similar.

Grade 10 Similar and Congruent Figures

A triangle where

$ang B = 30°$ will be similar to a triangle where

$ang C = 60°.$

Always
If the side lengths are the same
If they are right triangles
Never

Grade 10 Similar and Congruent Figures CCSS: HSG-SRT.A.3

$Delta CDE$ ,

$m ang C = 35°$ and

$m ang E = 100°$ . In

$Delta XYZ$ ,

$m ang X = 100°$ and

$m ang Y = 45°$ . Which of the following is correct?

$Delta CDE \ ~ \ Delta XYZ$
$Delta CDE \ ~ \ Delta ZYX$
$Delta CDE \ ~ \ Delta ZXY$
$Delta CDE \ ~ \ Delta YZX$

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

$Delta ABC$ and

$Delta ACD$ are both right triangles, where

$ang B$ and

$ang D$ are right angles, and

$ang BAC ~= ang CAD$ . If

$AB = 24 \ "units"$ and

$AC = 25 \ "units"$ , what is the value of

$CD ?$ .

Not enough information.
49 units
24 units
7 units

Grade 10 Similar and Congruent Figures CCSS: HSG-SRT.A.3

$Delta ABC$ is a right, isosceles triangle and

$m ang A = 90°$ .

$Delta XYZ$ is also a right, isosceles triangle and

$m ang X = 90°$ . Which of the following is correct?

$Delta ABC \ ~ \ Delta XYZ$
$Delta ABC \ ~ \ Delta ZYX$
These two triangles are not similar.
These two triangles may or may not be similar, but there is not enough information to be certain.

Grade 10 Similar and Congruent Figures

In the following diagram, quadrilaterals ABED and BFDC are both parallelograms. Match the sides or angles which are congruent.

__	$bar{AB}$	A.	$ang 2$
__	$ang A$	B.	$bar{ED}$
__	$ang 1$	C.	$ang E$
__	$bar{AC}$	D.	$ang DFE$
__	$ang BCA$	E.	$bar{FE}$

Grade 10 Similar and Congruent Figures CCSS: HSG-SRT.A.2

$Delta ABC \ ~ \ Delta A'B'C'$ ,

$AB = 3$ ,

$A'B' = 9$ , and

$BC = 5$ , what is the value of

$B'C' ?$

$11$
$15$
$5/3$
$25$

Grade 10 Similar and Congruent Figures CCSS: HSG-SRT.A.3

$Delta DEF$ ,

$m ang D = 50°$ and

$m ang E = 63°$ . In

$Delta RST$ ,

$m ang R = 50°$ and

$m ang S = 65°$ . Which of the following is correct?

$Delta DEF \ ~ \ Delta RST$
$Delta DEF \ ~ \ Delta SRT$
$Delta DEF \ ~ \ Delta RTS$
These two triangles are not similar.

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

In the following figure,

$ang A ~= ang C$ and

$ang ADB ~= ang CBD$ . If

$m ang A = x+15°$ ,

$m ang ADB = x-40°$ , and

$m ang CDB = x+25°$ , find the value of

$x$ . Round the answer to one decimal place if necessary.

$x = 60$
$x = 53.3$
$x = -4$
$x = 87.5$

Grade 10 Similar and Congruent Figures CCSS: HSG-SRT.A.3

$Delta EFG$ is an obtuse isosceles triangle,

$m ang E = 39°$ , and

$bar{EG}$ is the longest side.

$Delta JKL$ is also an obtuse isosceles triangle and

$m ang L = 102°$ . Which of the following is correct?

$Delta EFG \ ~ \ Delta JKL$
$Delta EFG \ ~ \ Delta JLK$
These two triangles are not similar.
These two triangles may or may not be similar, but there is not enough information to be certain.

Grade 10 Similar and Congruent Figures CCSS: HSG-SRT.A.2

Are these two triangles are similar?
Triangle 1: A = 125, C = 18
Triangle 2: B = 125, C = 35
Acute Triangle ABC v1

Yes, the triangles are similar.
No, the triangles are not similar.

Grade 10 Similar and Congruent Figures CCSS: HSG-SRT.A.2

Jennifer leaves her house walking in a direction 20 degrees East of North and walks for 20 minutes. She then walks 30 degrees South of East for 50 minutes at the same pace.
Tara goes for a jog and leaves home in a direction 60 degrees West of North. After 10 minutes she heads 70 degrees South of West for 25 minutes at the same pace.
If both Jennifer and Tara return straight home, will their paths form similar triangles?
Show your work.

There is not enough information
Yes
No
Only if they live in the same house

Grade 10 Similar and Congruent Figures CCSS: HSG-SRT.A.3

$Delta HJK$ is a right triangle with

$bar{HK}$ as the hypotenuse and

$m ang H = 53°$ .

$Delta QRS$ is also a right triangle, with

$bar{QS}$ as the hypotenuse and

$m ang S = 37°$ . Which of the following is correct?

$Delta HJK \ ~ \ Delta QRS$
$Delta HJK \ ~ \ Delta SRQ$
These two triangles are not similar.
These two triangles may or may not be similar, but there is not enough information to be certain.

Grade 10 Similar and Congruent Figures CCSS: HSG-SRT.A.3

$Delta ABC$ ,

$m ang A = m ang B = 50°$ . In

$Delta WXY$ ,

$m ang Y = 80°$ . Which of the following is correct?

$Delta ABC \ ~ \ Delta WXY$
$Delta ABC \ ~ \ Delta XYW$
These two triangles are not similar.
These two triangles may or may not be similar, but there is not enough information to be certain.

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

Anne is trying to determine the width of a river that flows from east to west. She is currently standing on the south side of the river, very near the river's edge. Directly across the river, almost touching the water, is a large tree. She knows that she can create two similar triangles to measure the width of the river. She begins walking due west for 21 ft, and then walks 10 ft south. Looking directly at the large tree she noticed earlier across the river, she walks towards the river in a north-easterly direction. When she arrives at the river, she sees that she is exactly 14 ft west of her original starting point. How wide is the river at the point from which she was originally standing? Round the answer to one decimal place if necessary.

20 ft
15 ft
9.8 ft
6.7 ft

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

Sam is standing near a tree. If Sam is 6 feet tall and casts an 11 foot shadow, and the tree casts a 30 foot shadow, how tall is the tree? Round the answer to 1 decimal place, if necessary.

2.2 ft
16.4 ft
55 ft
Not enough information.

Grade 10 Similar and Congruent Figures

A carpenter constructed a rectangular sandbox with a capacity of 10 cubic feet. if the carpenter were to make a similar sandbox twice as long, twice as wide, and twice as high as the first sandbox, what would be the capacity, in cubic feet, of the second sandbox?

Grade 10 Similar and Congruent Figures CCSS: HSG-CO.B.8

In triangles

$ABC$ and

$DEF,$

$bar(AC) = bar(ED)$ ,

$ang D= ang C$ , and

$ang B = ang F$ . The two triangles are congruent.

True
False

Grade 10 Similar and Congruent Figures

Two triangles with corresponding congruent angles are considered .

right
complementary
equilateral
similar
none of these are correct

Grade 10 Similar and Congruent Figures

Trapezoid LMNO is congruent to trapezoid QRST. Which side of QRST corresponds to LM?

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Tenth Grade (Grade 10) Similar and Congruent Figures Questions