Geometry Test Triangles Q2

R, S, and T are the vertices of one triangle. E, F, and D are the vertices of another triangle.  $m\angle R=50,\ m\angle S=100,\ m\angle F=50,\ m\angle D=30,\$  $\overline{RS}=4,$  and  $\overline{EF}=4.$ Are the two triangles congruent? If yes, explain and tell which segment is congruent to  $\overline{RT.}$  

• yes, by AAS;  $\overline{ED}$  
  

• yes, by ASA;  $\overline{FD}$  
  

• yes, by SAS;  $\overline{ED}$  
  

• No, the two triangles are not congruent
  

In the figure,  $\Delta ABC\sim\Delta A'B'C'.$  Which statement is true of the transformation from  $\Delta ABC\sim\Delta A'B'C'?$  

• The measures of all corresponding angles change by a scale factor of  $\frac{1}{2}.$  
  

• The measures of all corresponding angles change by a scale factor of 2.
  

• The lengths of all corresponding sides change by a scale factor of  $\frac{1}{2}.$  
  

• The lengths of all corresponding sides change by a scale factor of 2.
  

If  $\Delta ABC\cong\Delta XYZ,$ which of the following can you NOT conclude as being true?

•  $\overline{BC}\cong\overline{YZ}$  

•  $\overline{AB}\cong\overline{XZ}$  

•  $\angle B\cong\angle Y$  

•  $\angle A\cong\angle X$  

Supply the reasons missing from the proof.
Given:  $\overline{AB}\cong\overline{AC},\ \angle BAD\cong\angle CAD$ 
Prove:  $\overline{AD}$ bisects  $\overline{BC}$  

• ASA; Corresponding Parts of Congruent Triangles are Congruent.
  

• SAS; Corresponding Parts of Congruent Triangles are Congruent.
  

• SAS; Reflexive Property
  

• SSS; Reflexive Property
  

Based on the given information, what can you conclude, and why?
Given:  $\angle H\cong\angle L,\ \overline{HJ}\cong\overline{JL}$ 

•  $\Delta HIJ\cong\Delta JLK$  by ASA
  

•  $\Delta HIJ\cong\Delta LKJ$  by ASA
  

•  $\Delta HIJ\cong\Delta JLK$  by SAS
  

•  $\Delta HIJ\cong\Delta LKJ$  by SAS
  

Supply the missing reasons to complete the proof.
Given:  $\angle P\cong\angle S$ and  $\overline{PR}\cong\overline{SR}$ 
Prove:  $\overline{QR}\cong\overline{TR}$  

• ASA; Corresponding Parts of Congruent Triangles are Congruent.
  

• SAS; Corresponding Parts of Congruent Triangles are Congruent.
  

• ASA; Substitution
  

• AAS; Corresponding Parts of Congruent Triangles are Congruent.
  

Which can be the side lengths of a triangle?

Identify one or more choices that best complete the statement.

• 3, 5, 7

• 1, 2, 1

• 1, 1, 1

• 4, 4, 7

• 4, 6, 10

Use the information in the diagram to determine the height of the tree to the nearest foot.

• 80 ft

• 88 ft

• 72 ft

• 92 ft

Michele wanted to measure the height of her school's flagpole. She placed a mirror on the ground 48 feet from the flagpole, then walked backwards until she was able to see the top of the pole in the mirror. Her eyes were 5 feet above the ground and she was 12 feet from the mirror. Using similar triangles, find the height of the flagpole to the nearest tenth of a foot.

• 24 ft

• 25 ft

• 20 ft

• 12 ft

 $ABCD\sim GHJDF.$ Complete the statements.
 a.  $\angle H\cong_{ }$  ?
 b.  $\frac{GH}{DJ}=\frac{AB}{?}$  

•  $\angle B;\ DF$  

•  $\angle E;\ DF$  

•  $\angle B;\ DC$  

•  $\angle E;\ DC$