Question 1(Multiple Choice Worth 1 points)

Question

(03.02 MC)

Which of the following statements is true only if triangles EFI and GFH are similar?

Line segments EG and HI intersect at point F, forming triangles EFI and HFG. Line a intersects with both triangles at point F.

two segment FI equals three segment FH
segment FH over segment FI equals segment HG over segment IE
Points E, F, and G are collinear
∠F ≅ ∠F
Question 2(Multiple Choice Worth 1 points)
(03.02 MC)

ΔABC was dilated from the origin by a scale factor to create ΔA′B′C′. Which of the following is true for the similar triangles?

Side BC is proportional to side AB.
Side BC is proportional to side B'C'.
Side BC is proportional to side CB.
Side BC is proportional to side A'B'.
Question 3(Multiple Choice Worth 1 points)
(03.02 LC)

Triangle BAC was rotated 90° clockwise and dilated at a scale factor of 2 from the origin to create triangle XYZ. Based on these transformations, which statement is true?

coordinate plane with triangles ACB and XYZ with A at negative 4 comma 4, C at negative 1 comma 3, B at negative 4 comma 0, X at 0 comma 8, Y at 8, comma 8, and Z at 6 comma 2

∠Z ≅ ∠A
∠B ≅ ∠Y
∠A ≅ ∠X
∠C ≅ ∠Z
Question 4(Multiple Choice Worth 1 points)
(03.02 MC)

ΔPQR is dilated from the origin at a scale factor of one half to create ΔP′Q′R′.

Select the option that completes the statement:

The triangles are ________ because their corresponding sides are ________ and their corresponding angles are ________.

congruent; similar; proportional
congruent; proportional; similar
similar; congruent; proportional
similar; proportional; congruent
Question 5(Multiple Choice Worth 1 points)
(03.02 MC)

coordinate plane with quadrilaterals ABCD and EFGH with A at 0 comma 0, B at 2 comma 0, C at 3 comma negative 2, D at negative 1 comma negative 2, E at 2 comma 4, F at 6 comma 4, G at 7 comma 2, and H at 1 comma 2

Are quadrilaterals ABCD and EFGH similar?

Yes, quadrilaterals ABCD and EFGH are similar because a translation of (x + 2, y + 4) and a dilation by the scale factor of 2 from point D′ map quadrilateral ABCD onto EFGH.
Yes, quadrilaterals ABCD and EFGH are similar because a translation of (x + 3, y + 4) and a dilation by the scale factor of 2 from point A′ map quadrilateral ABCD onto EFGH.
No, quadrilaterals ABCD and EFGH are not similar because their corresponding angles are not congruent.
No, quadrilaterals ABCD and EFGH are not similar because their corresponding segments are not proportional.
Question 6(Multiple Choice Worth 1 points)
(03.02 MC)

Triangle A″B″C″ is formed by a reflection over x = 1 and dilation by a scale factor of 2 from the origin. Which equation shows the correct relationship between ΔABC and ΔA″B″C″?

coordinate plane with triangle ABC at A negative 3 comma 3, B 1 comma negative 3, and C negative 3 comma negative 3

segment AB over segment A double prime B double prime equals one half
segment C double prime A double prime over segment CA equals one half
segment AB equals zero point two segment A double prime B double prime
segment C double prime A double prime equals zero point two segment CA
Question 7(Multiple Choice Worth 1 points)
(03.02 MC)

coordinate plane with triangles EFG and GHI with E at negative 6 comma 2, F at negative 2 comma 6, G at negative 2 comma 2, H at negative 2 comma 4, and I at 0 comma 2

Which set of transformations would prove ΔGFE ~ ΔGHI?

Translate ΔGHI by the rule (x − 2, y + 0), and reflect ΔG′H′I′ over x = −4.
Reflect ΔGHI over x = −2, and translate ΔG′H′I′ by the rule (x + 2, y + 0).
Translate ΔGHI by the rule (x + 0, y + 2), and dilate ΔG′H′I′ by a scale factor of 2 from point H.
Reflect ΔGHI over x = −2, and dilate ΔG′H′I′ by a scale factor of 2 from point G.
Question 8(Multiple Choice Worth 1 points)
(03.02 MC)

Triangle A″B″C″ is formed using the translation (x + 0, y + 2) and the dilation by a scale factor of 2 from the origin. Which equation explains the relationship between segment AC and segment A double prime C double prime?

coordinate plane with triangle ABC at A negative 3 comma 3, B 1 comma negative 3, and C negative 3 comma negative 3

segment AC over segment A double prime C double prime = 2
segment A double prime C double prime over segment AC = one half
segment AC = segment A double prime C double prime over 2
segment A double prime C double prime = segment AC over 2
Question 9(Multiple Choice Worth 1 points)
(03.02 MC)

ΔEFI is dilated by a scale factor of one third with the center of dilation at point F. Then, it is reflected over line a to create ΔHFG. Based on these transformations, which statement is true?

Line segments EG and HI intersect at point F, forming triangles EFI and HFG. Line a intersects with both triangles at point F.

segment FE = segment FH over 3, segment FI = segment FG over 3, and segment EI = segment HG over 3; ΔEFI ~ ΔHFG
segment FE = segment FG over 3, segment FI = segment FH over 3, and segment EI = segment HG over 3; ΔEFI ~ ΔGFH
segment FE over 3 = segment FG, segment FI over 3 = segment FH, and segment EI over 3 = segment HG; ΔEFI ~ ΔGFH
segment FE over 3 = segment FH, segment FI over 3 = segment FG, and segment EI over 3 = segment HG; ΔEFI ~ ΔHFG
Question 10(Multiple Choice Worth 1 points)
(03.02 LC)

Given triangles ABC and DEF, which statement explains a way to determine if the two figures are similar?

Verify corresponding pairs of angles are congruent by translation.
Verify corresponding pairs of sides are congruent by dilation.
Verify corresponding pairs of angles are congruent by dilation.
Verify corresponding pairs of sides are congruent by translation.
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Answer 1

Here are the answers to the multiple-choice questions based on geometry concepts involving similar triangles, transformations, and dilations:

Question 1: Which of the following statements is true only if triangles EFI and GFH are similar?

• Answer: segment FH over segment FI equals segment HG over segment IE

Question 2: ΔABC was dilated from the origin by a scale factor to create ΔA′B′C′. Which of the following is true for the similar triangles?

• Answer: Side BC is proportional to side B'C'.

Question 3: Triangle BAC was rotated 90° clockwise and dilated at a scale factor of 2 from the origin to create triangle XYZ. Based on these transformations, which statement is true?

• Answer: ∠C ≅ ∠Z

Question 4: ΔPQR is dilated from the origin at a scale factor of one half to create ΔP′Q′R′.

• Answer: similar; proportional; congruent

Question 5: Are quadrilaterals ABCD and EFGH similar?

• Answer: No, quadrilaterals ABCD and EFGH are not similar because their corresponding angles are not congruent.

Question 6: Triangle A″B″C″ is formed by a reflection over x = 1 and dilation by a scale factor of 2 from the origin. Which equation shows the correct relationship between ΔABC and ΔA″B″C″?

• Answer: segment AB equals zero point two segment A double prime B double prime

Question 7: Which set of transformations would prove ΔGFE ~ ΔGHI?

• Answer: Reflect ΔGHI over x = −2, and dilate ΔG′H′I′ by a scale factor of 2 from point G.

Question 8: Triangle A″B″C″ is formed using the translation (x + 0, y + 2) and the dilation by a scale factor of 2 from the origin. Which equation explains the relationship between segment AC and segment A double prime C double prime?

• Answer: segment A double prime C double prime over segment AC = one half

Question 9: ΔEFI is dilated by a scale factor of one third with the center of dilation at point F. Then, it is reflected over line a to create ΔHFG. Based on these transformations, which statement is true?

• Answer: segment FE = segment FH over 3, segment FI = segment FG over 3, and segment EI = segment HG over 3; ΔEFI ~ ΔHFG

Question 10: Given triangles ABC and DEF, which statement explains a way to determine if the two figures are similar?

• Answer: Verify corresponding pairs of angles are congruent by translation.

Please review and adjust any answers according to any additional context or specifications from your coursework, but these are based on standard geometric principles.