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This printable supports Common Core Mathematics Standard HSG-SRT.B.5

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# Applying Similar and Congruent Triangles (Grade 10)

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## Applying Similar and Congruent Triangles

1.
In $Delta ABC$, $AC = 5 \ "units"$ and $AB = 12 \ "units"$. Find $AD$. Round the answer to one decimal place, if necessary.
1. 0.8 units
2. 2.1 units
3. 10.9 units
4. 12 units
2.
In $Delta ABC$, $AB = 15 \ "units"$ and $CB = 10 \ "units"$. Find the value of $BD$. Round the answer to one decimal place, if necessary.
1. 15 units
2. 11.2 units
3. 6.7 units
4. 1.3 units
3.
In $Delta ABC$, $AC = x+6 \ "units"$, $AD = x \ "units"$, and $DB = x + 28 \ "units"$. What is the value of $x ?$
1. $x=2$
2. $x=-18$
3. $x=9/4$
4. $x = -13/2 + 1/2sqrt(193)$
4.
In the circle pictured below with center $O$, $bar{AD}$ is tangent to the circle and $bar{AB}$ is a diameter. If $ang ADO ~= ang CAB$, $CB = 5 \ "units"$ ($bar{CB}$ is not drawn), and $OB = 4 \ "units"$, what is the length of $bar{OD} ?$
1. Not enough information.
2. $32/5 \ "units"$
3. $8 \ "units"$
4. $10 \ "units"$
5.
In the circle pictured below point $O$ is the center, $bar{AB}$ is a diameter, and $bar{AD}$ is tangent to the circle. If $ang CAB ~= ang ADO$, $CB = 2x \ "units"$ ($bar{CB}$ is not drawn), $AB = 2x+4 \ "units"$, and $OD = x + 16/3 \ "units"$, what is the value of $x ?$
1. $x = 16/3$
2. $x = 16/9$
3. $x=3$
4. $x = -10/3 +2/3sqrt(34)$
6.
$Delta ABC$ 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 $CD ?$.
1. Not enough information.
2. 49 units
3. 24 units
4. 7 units
7.
In the figure below, $bar{AB} ~= bar{CE}$, $ang BAF ~= ang CED$, and $ang AFB$ and $ang EDC$ are right angles. If $AB = 13 \ "units"$, $BF=12 \ "units"$, $FD=20 \ "units"$, what is the value of $FE ?$
1. Not enough information.
2. 8 units
3. 15 units
4. 25 units
8.
In the figure below, quadrilateral ABED is a parallelogram. If $ang 1 ~= ang 2~= ang BCF ~= ang CFD$, $CF = 6 \ "units"$ ($bar{CF}$ is not drawn), and $BF = 4 \ "units"$, what is the perimeter of parallelogram ABED?
1. 20 units
2. 28 units
3. 32 units
4. Not enough information.
9.
In the figure below, $Delta ABF ~= Delta ECD$ and $FBCD$ is a rectangle. If $AF = 8 \ "units"$, $AB = 17 \ "units"$, and $FE = 27 \ "units"$, what is the perimeter of rectangle $FBCD ?$ Round the answer to one decimal place if necessary.
1. 100 units
2. 107.6 units
3. 85 units
4. 84 units
10.
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.
1. $x = 60$
2. $x = 53.3$
3. $x = -4$
4. $x = 87.5$
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