Tenth Grade (Grade 10) Similar and Congruent Figures Questions for Tests and Worksheets

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Grade 10 Similar and Congruent Figures CCSS: HSG-SRT.B.4

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What is the missing reason in step 6?

Definition of a right triangle
Pythagorean Identity
Sum of angles in a triangle equals 180°
Given

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

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The previous questions have shown that, if two angles of one triangle are congruent to two angles of another triangle, then all the conditions of similar triangles are met (all angles are congruent and the ratios of the corresponding sides are equal). What would change if the assumption

$AB < PQ$ was changed? Choose all correct answers.

If $AB = PQ$ , then the two triangles would be congruent.
If $AB = PQ$ , then the two triangles must be coincident before any transformations are performed.
If $AB > PQ$ , the two triangles would not be similar or congruent.
If $AB > PQ$ , the triangles would still be similar, and only minor changes to the math in showing them to be similar would be required.

Grade 10 Similar and Congruent Figures

Congruent segments are segments that are the same length.

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

A triangle with vertices J, K, and L has the following side length and angle measure:

$JK = 10$ and

$m ang J = 49°$ . A triangle with vertices P, Q, and R has the following side length and angle measure:

$PQ = 5$ and

$m ang P = 49°$ . These two triangles must be similar.

True
False

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

$Delta FGH$ ,

$m ang G = 73°$ and

$m ang F = 42°$ . If

$Delta F'G'H' \ ~ \ Delta FGH$ , find

$m ang H'$ .

65°
42°
73°
Not enough information.

Grade 10 Similar and Congruent Figures

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

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

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Using the previous result, it can be shown that

$(PQ) / (A_4B_4) = (QR)/(B_4C_4)$ . Which of the following dilations would transform point

$A_4$ to point

$P ?$ Note: this dilation, applied to

$Delta A_4B_4C_4$ , would also transform point

$C_4$ to

$R$ .

A dilation of factor $PQ$ centered at point Q.
A dilation of factor $(PQ)/(A_4B_4)$ centered at point Q.
A dilation of factor $(PQ)/(A_4B_4)$ centered at the origin.
A dilation of factor $A_4B_4$ centered at the origin.

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

$Delta BCD$ ,

$m ang B = 53°$ and

$m ang D = 74°$ . In

$Delta LMN$ ,

$m ang L = 53°$ and

$m ang M = 53°$ . Which of the following is correct? Choose all correct answers.

$Delta BCD \ ~ \ Delta LMN$
$Delta BCD \ ~ \ Delta MLN$
$Delta BCD \ ~ \ Delta LNM$
$Delta BCD \ ~ \ Delta NML$

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

In triangle

$ABC$

$angA=60deg$ and

$ang C=90deg$ . In triangle

$DEF$

$angE=30deg$ and

$ang D=80deg$ . The two triangles are similar.

True
False

Grade 10 Similar and Congruent Figures CCSS: HSG-SRT.B.4

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What is the missing reason in step 14?

Ratios of corresponding sides in similar triangles are equal
Division Property of Equality
Segment Division Postulate
Transitive Property of Equality

Grade 10 Similar and Congruent Figures CCSS: HSG-SRT.B.4

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What is the missing reason in step 9?

Definition of a midpoint
Given
Segment Addition Postulate
Substitution Property of Equality

Grade 10 Similar and Congruent Figures CCSS: HSG-SRT.B.4

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What is the missing reason in step 3?

Definition of a midpoint
Given
Segment Equality Postulate
Substitution Property of Equality

Grade 10 Similar and Congruent Figures CCSS: HSG-SRT.B.4

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What is the missing reason in step 8?

Ratios of corresponding sides of similar triangles are equal
Division Property of Equality
Substitution Property of Equality
Corresponding sides of congruent triangles are congruent

Grade 10 Similar and Congruent Figures CCSS: HSG-SRT.B.4

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What is the missing reason in step 32?

Segment Addition Postulate
Given
Midpoint of a line segment
Perpendicular Bisector Theorem

Grade 10 Similar and Congruent Figures CCSS: HSG-SRT.B.4

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What is the missing statement in step 27?

$Delta ABC \ ~ \ Delta CBD$
$Delta ABC \ ~ \ Delta CDB$
$Delta ABC \ ~ \ Delta DBC$
$Delta ABC \ ~ \ Delta DCB$

Grade 10 Similar and Congruent Figures CCSS: HSG-SRT.B.4

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What is the missing reason in step 18?

Given
Angle Addition Postulate
Consecutive Interior Angles Postulate
Sum of the acute angles in a right triangle is 90°

Grade 10 Similar and Congruent Figures CCSS: HSG-SRT.B.4

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What is the missing reason in step 9?

Addition Property of Equality
Transitive Property of Equality
Subtraction Property of Equality
Corresponding angles of congruent triangles are congruent

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

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Given the previous result, it can be concluded that

$bar{A_4 C_4} \ "||" \ bar{PR}$ . Which of the following is the reason why?

If two lines are cut by a transversal and corresponding angles are congruent, then the lines are parallel.
If two lines are cut by a transversal and alternate interior angles are congruent, then the lines are parallel
If two lines are cut by a transversal and alternate exterior angles are congruent, then the lines are parallel
If two lines are cut by a transversal and the sum of the measures of consecutive interior angles is 180°, then the lines are parallel

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

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Since only rigid transformations have been applied,

$Delta ABC ~= Delta A_4B_4C_4$ . Given this, and all given information, which of the following is/are correct? There may be more than one correct answer.

$ang B_4A_4C_4 ~= ang A ~= ang P$
$ang B_4 ~= ang B ~= ang Q$
$ang A_4C_4B_4 ~= ang C ~= ang R$
$bar{AC} ~= bar{A_4C_4} ~= bar{PR}$

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

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Which of the following shows that

$ang C ~= ang R ?$

$m ang A + m ang B + m ang C = 180°$ and $m ang P + m ang Q + m ang R = 180°$
$m ang C = 180° - m ang A - m ang B = 180° - m ang P - m ang Q = m ang R$
$m ang C = m ang A + m ang B = m ang P + m ang Q = m ang R$
$m ang C = -m ang A - m ang B = -m ang P - m ang Q = m ang R$

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Tenth Grade (Grade 10) Similar and Congruent Figures Questions