Unit 4 Review

In the figure below, segments AB || DC and AC || BD. Why are ΔABD and ΔDCA congruent?

• SSS≅

• SAS≅

• ASA≅

• AAS≅

Two men are standing by a palm tree and are looking at the exposed treasure located on the rock across from the canyon. They have a map that lists the distances between certain items. Find the distance between the men and the treasure.

• 93ft

• 103ft

• 45ft

• 60ft

Joe wants to find the height of a pine tree for a math class project. Joe is 6 ft tall. He stands 12 ft away from the tree and his shadow is 8 ft long. What is the correct proportion to find X?

• x=15

• x=20

• x=4

• x=6

In the diagram below Δ MNL ≈ Δ XZY. What is the length of ZX?

• ZX=7

• ZX=35

• ZX=40

• ZX=10

Analyze the following triangles and determine the similarity postulate that makes the triangles similar.

• AA~

• SSS~

• SAS~

• Triangles are not similar.

A building is 33 ft tall and casts a shadow that is 11 ft long. If a neighboring building casts a shadow that is 8 ft long at the same time, how tall is the building?

• The height of the building is 33ft

• The height of the building is 11ft

• The height of the building is 264ft

• The height of the building is 24ft

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

The diagonals of parallelograms bisect each other.

1) Name the two diagonals of the parallelogram at right.

​ (a)  

2) Complete the statement below to show that the diagonals bisect each other. AE≅​ ​ (b)   and DE≅​ (c)  

• AC and BD
• EC
• EB

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.

• △ABC≅△CDA

• 
• Reflexive Property of Congruence

• 
• Definition of Parallelogram

• 
• Congruent Parts of Congruent Triangles

• 
• AC is a transversal of AD and BC

• 

Use the parallelogram to determine which of the following values are correct. Select three that apply.

• x=4.5

• y=120

• <A=60

• <B=120

• <c=60