Math 2 - Unit 2 Review

Math 2 - Unit 2 Review

Mr. Coleman

Unit 2 - Congruence and Similarity

Poll

Which of our lessons from Unit 2 do you feel like you need to work on the most?

• Lesson 2.1: Parallel Lines and Transversals

• Lesson 2.2: Congruence and CPCTC

• Lesson 2.3: Congruent Triangles

• Lesson 2.4: Similar Triangles

Lesson 2.1: Parallel Lines and Transversals

• Angle pair relationships

• Solving for missing angles

• Proofs with parallel lines

Angle Relationships

• Corresponding Angles (1 and 5, 2 and 6, 3 and 7, 4 and 8) - CONGRUENT

• Alternate Interior Angles (3 and 6, 4 and 5) - CONGRUENT

• Alternate Exterior Angles (1 and 8, 2 and 7) - CONGRUENT

• Consecutive Interior Angles (3 and 5, 4 and 6) - SUPPLEMENTARY

Multiple Select

From the diagram shown, state all angles that would be CONGRUENT to Angle 1.

• Angle 3

• Angle 4

• Angle 5

• Angle 6

• Angle 8

Solving for Missing Angles

• Identify the angle to be solved

• Look for relationships with known angles

• Use relationships to solve for the missing value by setting them equal to each other (congruent) or their sum equal to 180 (supplementary)

Fill in the Blanks

Solve for the values of x and y from the diagram shown.

Proofs with Parallel Lines

• Case 1: Using parallel line relationships to prove congruent angle pairs

• Case 2: Using angle relationships to prove lines are parallel

Multiple Choice

Based on the diagram shown, what reason would justify verifying that Angle 1 is congruent to Angle A?

• Alternate interior angles

• Alternate exterior angles

• Corresponding angles

• Vertical angles

Lesson 2.2: Congruence and CPCTC

• Definition of congruence

• Identifying corresponding parts of figures

• Using CPCTC to find missing values

Open Ended

What does it mean for two figures to be congruent? Be as detailed as possible in your explanation.

Multiple Select

If we are told that

 $\Delta VRT\ \cong\ \Delta MNL$  , which of the following congruence statements are valid?

•  $\overline{RT}\ \cong\ \overline{MN}$  

•  $\angle TRV\ \cong\ \angle LNM$  

•  $\overline{VT}\ \cong\ \overline{ML}$  

•  $\angle TVR\ \cong\ \angle NML$  

•  $\overline{LN}\ \cong\ \overline{TR}$  

Multiple Choice

For the diagram provided, use the given information to solve for the value of x.

• x = 20

• x = 15

• x = -10

• x = 2

Lesson 2.4: Congruent Triangles

• Triangle Congruence Theorems

• Identifying Applicable Theorems

• Proving Triangles Congruent

Multiple Choice

Which of the following is NOT a valid triangle congruence theorem?

• ASA

• SSS

• SSA

• AAS

• SAS

Multiple Choice

Which triangle congruence shortcut verifies the two given triangles are congruent?

• SSS

• ASA

• SAS

• AAS

• HL

Multiple Select

Which of the following pieces of information would allow you to prove these triangles congruent by ASA?

• $\overline{DE}\ \cong\ \overline{BE}$

• $\overline{AB}\ \parallel\ \overline{CD}$

• $\angle AEB\ \cong\ \angle CDE$

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

Lesson 2.4: Similar Triangles

• Definition of Similarity

• Triangle Similarity Theorems

• Applying Similar Figures

• Proving Triangles Similar

Multiple Choice

Given the image shown in the diagram, which triangle similarity theorem would prove

 $\Delta APQ\ \sim\ \Delta ABC$  ? 

• AA

• SSS

• ASA

• Triangles cannot be proven similar. 

Multiple Choice

Which of the following is NOT a theorem to prove triangles are similar?

• AA Theorem

• SAS Theorem

• ASA Theorem

• SSS Theorem

Fill in the Blanks

For the given figure, find the measure of h assuming that the triangles are similar.

Multiple Select

Which of the following statements must be true for two triangles to be similar?

• Corresponding sides congruent

• Corresponding angles congruent

• Corresponding sides proportional in length

• Corresponding angles proportional in measure