ASUPD Geometry Unit D Check for Understanding

Label the blank triangle with the corresponding triangle part.

a

b

c

d

e

f

||

))

)

|

)))

|||

Tags

CCSS.HSG.CO.B.7

Prove the following theorem by completing the paragraph proof: "If a quadrilateral is a parallelogram, then the opposite sides are congruent.

By the ​ ​ (a)   , AB || CD and BC || AD. Let AC be the transversal of AB and DC. So ∠A ≅ ∠C and ∠B ≅ ∠D by the alternate interior angles theorem. AC ≅ AC by the​ (b)   . ΔABC ≅ ΔCDA by ​ (c)   congruence criterion. AB≅CD and BC≅AD by ​ (d)   ."

A​

• congruent parts of congruent triangles

• definition of parallelogram
• Reflexive Property of Congruence
• SAS≅
• SSS≅
• ASA≅
• Congruent Parts of Congruent Triangles

Tags

CCSS.HSG.C.A.3

A parallelogram ABCD is shown. Anna is asked to prove that AB≅DC and AD≅BC. Help her complete her proof by using the given statements and reasons under the figure. Fill in the missing steps and reasons in the proof provided.

• Reflexive Property of Congruence

• 
• Congruent Parts of Congruent Triangles

• 
• AC is a transversal of AD and BC

• 
• △ABC≅△CDA

• 
• Definition of Parallelogram

• 

Tags

CCSS.HSG.CO.C.11

The figure is a parallelogram.

m∠x =​ (a)  

m∠y =​ (b)  

m∠z =​ (c)  

• 55°
• 125°
• 65°
• 120°
• 115°
• 180°
• 35°

Tags

CCSS.HSG.CO.C.11

Determine the correct reason for statement #4.

• opposite sides of a parallelogram are congruent theorem

• all sides are parallel

• sides are congruent

• sides are supplementary

Tags

CCSS.HSG.CO.C.11

A ​ (a)   ​ ​is a logical ​ (b)  

of statements and ​ (c)   used to ​ (d)   that a ​ (e)   mathematical concept or idea is true.​

• proof
• set
• reasons
• prove
• given

Fill in the missing proofs.

• Transitive Property, SAS(Side-Angle-Side)
• Reflexive Property, SAS(Side-Angle-Side)
• Reflexive Property, Vertical Angles Thm.
• Transitive Property, SSS(Side-Side-Side)

Tags

CCSS.HSG.CO.C.9

What is the "statement" for step 2 of the proof?

• ∆BAC≅∆DAC
• BC=DC
• ∡B≅∡D
• ∡BAC≅∡DAC

Tags

CCSS.HSG.CO.C.9

What is the "reason" for step 4 of the proof?

• proof
• AAS
  ≅ Thrm
• ASA
  ≅ Thrm
• SAS
  ≅ Thrm

Tags

CCSS.HSG.SRT.B.5

What is the "statement" for step 3 of the proof? 

• ∡EDA≅∡DCB
• ∡AED≅∡BEC
• DE=CE
• ∡AED≅∡CED

Tags

CCSS.HSG.SRT.B.5