Applying Similar and Congruent Triangles (Grade 10)

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Applying Similar and Congruent Triangles

1. 
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.
Right Triangle ABCD
  1. 0.8 units
  2. 2.1 units
  3. 10.9 units
  4. 12 units
2. 
In [math]Delta ABC[/math], [math]AB = 15 \ "units"[/math] and [math]CB = 10 \ "units"[/math]. Find the value of [math]BD[/math]. Round the answer to one decimal place, if necessary.
Right Triangle ABCD
  1. 15 units
  2. 11.2 units
  3. 6.7 units
  4. 1.3 units
3. 
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]
Right Triangle ABCD
  1. [math]x=2[/math]
  2. [math]x=-18[/math]
  3. [math]x=9/4[/math]
  4. [math]x = -13/2 + 1/2sqrt(193)[/math]
4. 
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]
Circle ABCD
  1. Not enough information.
  2. [math]32/5 \ "units"[/math]
  3. [math]8 \ "units"[/math]
  4. [math]10 \ "units"[/math]
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]
Circle ABCD
  1. [math]x = 16/3[/math]
  2. [math]x = 16/9[/math]
  3. [math]x=3[/math]
  4. [math]x = -10/3 +2/3sqrt(34)[/math]
6. 
[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].
Diamond ABCD
  1. Not enough information.
  2. 49 units
  3. 24 units
  4. 7 units
7. 
In the figure below, [math]bar{AB} ~= bar{CE}[/math], [math]ang BAF ~= ang CED[/math], and [math]ang AFB[/math] and [math]ang EDC[/math] are right angles. If [math]AB = 13 \ "units"[/math], [math]BF=12 \ "units"[/math], [math]FD=20 \ "units"[/math], what is the value of [math]FE ?[/math]
Trapezoid ABCDEF
  1. Not enough information.
  2. 8 units
  3. 15 units
  4. 25 units
8. 
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?
Parallelogram ABCDEF v1
  1. 20 units
  2. 28 units
  3. 32 units
  4. Not enough information.
9. 
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.
Trapezoid ABCDEF
  1. 100 units
  2. 107.6 units
  3. 85 units
  4. 84 units
10. 
In the following figure, [math]ang A ~= ang C[/math] and [math]ang ADB ~= ang CBD[/math]. If [math]m ang A = x+15°[/math], [math]m ang ADB = x-40°[/math], and [math]m ang CDB = x+25°[/math], find the value of [math]x[/math]. Round the answer to one decimal place if necessary.
Parallelogram ABCD v4
  1. [math]x = 60[/math]
  2. [math]x = 53.3[/math]
  3. [math]x = -4[/math]
  4. [math]x = 87.5[/math]

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