Triangles

Complete the proof.
Given: $\overline{XP}\parallel\overline{WQ}$ 
Prove: $\Delta XZP\sim\Delta WZQ$ 

We are given that  $\overline{XP}\parallel\overline{WQ};\$ 
therefore,  $\angle ZXP\cong\angle ZWQ$  and

 $\angle ZPX\cong\angle ZQW$  by the

• Corresponding Angles Postulate
  

• Alternate Interior Angles Theorem
  

• Alternate Exterior Angles Theorem
  

• Same-Side Interior Angles Postulate
  

Tags

CCSS.HSG.SRT.A.2

 Complete the proof.
Given:  $\overline{XP}\parallel\overline{WQ}$ 

Prove:  $\Delta XZP\sim\Delta WZQ$ 

We are given that  $\overline{XP}\parallel\overline{WQ};\ therefore,\ \angle ZXP\cong\angle ZWQ\ and\$ 

 $\angle ZPX\cong\angle ZQW$ 

Then we can conclude that  $\Delta XZP\sim\Delta WZQ$  by

• SSS

• AA

• SAS

• ASA

Tags

CCSS.HSG.SRT.B.5

Which statement regarding the triangles pictured is true?

• The triangles are similar because of the Angle-Angle Similarity Criterion.

• The triangles are similar because of the Side-Angle-Side Similarity Criterion.

• The triangles are similar because of the Side-Side-Side Similarity Criterion

• The triangles are not similar.

Tags

CCSS.HSG.SRT.B.5

What additional information is needed to prove the triangles are similar by the SAS Similarity Criterion?

• $\angle H\cong\angle R$

• $\angle F\cong\angle S$

• $\angle G\cong\angle I$

• $\angle G\cong\angle S$

Tags

CCSS.HSG.SRT.B.5

Find the value for m that makes  $\Delta HFG\cong\Delta HFK$ by SSS.

• m = 5
  

• m = 3

• m = 4
  

• m = 8
  

Tags

CCSS.HSG.SRT.B.5

Find the value for x that make  $\Delta GHM\cong\Delta MPG$ by SSS.

• x = 1
  

• x = 3
  

• x = 4
  

• x = 8
  

Tags

CCSS.HSG.SRT.B.5

Find the value for y that make  $\Delta GHM\cong\Delta MPG$ by SSS.

• y = 7
  

• y = 11
  

• y = 13
  

• y = 8
  

Tags

CCSS.HSG.SRT.B.5

Find the value of x that makes the triangles congruent by AAS.

• $x=67\degree$

• $x=89\degree$

• $x=64\degree$

• $x=87\degree$

Tags

CCSS.HSG.SRT.B.5

Which statement best explains why  $\Delta ABC\cong\Delta IEC?$  

•  $\Delta ABC$  can be mapped onto  $\Delta IEC$  using a dilation.
  

•  $\Delta IEC$  can be mapped onto  $\Delta ABC$  using a reflection.
  

•  $\Delta ABC$  can be mapped onto  $\Delta IEC$  using a translation.
  

•  $\Delta ABC$  can be mapped onto  $\Delta IEC\$  using a rotation.
  

Tags

CCSS.8.G.A.2

CCSS.HSG.CO.B.6

Consider the right triangle DUE and it's reflection,  $\Delta FHG,$  as pictured.

Select all reasons that cannot be used to justify why  $\Delta DUE\cong\Delta FHG.$  

• AAA

• SAS

• SSA

• ASA

• CPCTC

Tags

CCSS.HSG.SRT.B.5