Geometry

User: Aariella Albury E-Mail: [email protected] In Course: GEO ( 4498) Instructor: Kelly Dale

Exam: 05.02 Module Five Quiz

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Question 1 (Multiple Choice Worth 5 points) (05.01 MC)

In ΔABC shown below, :

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The following flowchart proof with missing statements and reasons proves that if a line intersects two sides of a triangle and divides these sides proportionally, the line is parallel to the third side:

Which reason can be used to fill in the numbered blank space?

1. ∠BDE ≅ ∠BAC 2. Corresponding Angles Postulate

1. ∠BDE ≅ ∠BAC 2. Corresponding Parts of Similar Triangles

1. ∠BDE ≅ ∠BCA 2. Alternate Exterior Theorem

1. ∠BDE ≅ ∠BCA 2. Corresponding Parts of Similar Triangles

Question 2 (Multiple Choice Worth 5 points) 

(05.01 MC)

Use ΔPQR below to answer the question that follows:

Which fact is not used to prove that PQR is similar to STR?

Segments ST and PQ are parallel.

Angle P is congruent to itself due to the reflexive property.

RP is a transversal line passing ST and PQ.

Angles RTS and RQP are congruent due to the Corresponding Angles Postulate.

Question 3 (Multiple Choice Worth 5 points) (05.01 MC)

Given: ΔABC is a right triangle. Prove: a + b = c

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2 2 2

The following two-column proof with missing justifications proves the Pythagorean Theorem using similar triangles:

Statement Justification

Draw an altitude from point C to  

Let = a = b = c = h = x = y

 

y + x = c  

 

a = cy; b = cx  

a + b = cy + b  

a + b = cy + cx  

a + b = c(y + x)  

a + b = c(c)  

a + b = c  

Which is not a justification for the proof?

2 2

2 2 2

2 2

2 2

2 2

2 2 2

Pieces of Right Triangles Similarity Theorem

Side-Side-Side Similarity Theorem

Substitution

Addition Property of Equality

Question 4 (Multiple Choice Worth 5 points) (05.01 MC)

In ΔABC shown below, is parallel to :

The following two-column proof with missing statements and reasons proves that if a line parallel to one side of a triangle also intersects the other two sides, the line divides the sides proportionally:

Statement Reason

1. 1. Given

2. is a transversal that intersects two parallel lines.

2. Conclusion from Statement 1.

3. 3.

4. ∠B ≅ ∠B 4. Reflexive Property of Equality

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5. 5.

6. 6. Converse of the Side-Side-Side Similarity Theorem

Which statement and reason accurately completes the proof?

3. ∠BDE ≅ ∠BAC; Corresponding Angles Postulate 5. ΔBDE ~ ΔBAC; Angle-Angle (AA) Similarity Postulate

3. ΔBDE ~ ΔBAC; Corresponding Angles Postulate 5. ∠BDE ~ ∠BAC; Angle-Angle (AA) Similarity Postulate

3. ∠BDE ≅ ∠BAC; Congruent Angles Postulate 5. ΔBDE ~ ΔBAC; Angle-Angle (AA) Similarity Postulate

3. ∠BDE ≅ ∠BAC; Congruent Angles Postulate 5. ΔBDE ~ ΔBAC; Side-Angle-Side (SAS) Similarity Postulate

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