Geometry Honors: 03.02 Similarity

Decide whether the triangles are similar. If so, determine the appropriate expression to solve for x. The triangles are not similar; no expression for x can be found. ΔABC ~ ΔDEF; x = r . w/u ΔABC ~ ΔEFD; x = r . w/u ΔABC ~ ΔEFD; x = r . w/z

!!NOT!! ΔABC ~ ΔEFD; x = r . w/z

Triangle A″B″C″ is formed by a reflection over x = −3 and dilation by a scale factor of 3 from the origin. Which equation shows the correct relationship between ΔABC and ΔA″B″C′?

Line segment AB/ Line segment A"B" = 1/3

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 line segment AC and line segment A"C"?

Line segment AC = Line segment A"C"/2

Given trapezoids QRST and WXYZ, which statement explains a way to determine if the two figures are similar?

Verify corresponding pairs of sides are proportional by dilation.

ΔPQR is dilated from the origin at a scale factor of 1/2 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 ________.

similar; proportional; congruent

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? ∠C ≅ ∠X ∠C ≅ ∠Y ∠A ≅ ∠Y ∠A ≅ ∠X

∠A ≅ ∠Y

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

∠E ≅ ∠G

ΔHFG is dilated by a scale factor of 2 with the center of dilation at point F. Then, it is reflected over line a to create ΔEFI. Based on these transformations, which statement is true?

Line segment FG = line segment FI, line segment FH = 1/2 line segment FE, and line segment HG = 1/2 line segment EI ; ΔHFG ~ ΔEFI

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.

No, quadrilaterals ABCD and EFGH are not similar because their corresponding segments are not proportional.

Which set of transformations would prove ΔQRS ~ ΔUTS? Reflect ΔUTS over y = 2, and dilate ΔU′T′S′ by a scale factor of 2 from point S. Reflect ΔUTS over y = 2, and translate ΔU′T′S′ by the rule (x − 2, y + 0). Translate ΔUTS by the rule (x + 0, y + 6), and reflect ΔU′T′S′ over y = 6. Translate ΔUTS by the rule (x − 2, y + 0), and reflect ΔU′T′S′ over y = 2.

Reflect ΔUTS over y = 2, and dilate ΔU′T′S′ by a scale factor of 2 from point S.

A pool company is creating a blueprint for a family pool and a similar dog pool for a new client. Which statement explains how the company can determine whether pool STUV is similar to pool WXYZ?

Translate WXYZ so that point W of WXYZ lies on point S of STUV, then dilate WXYZ by the ratio LS TS/LS XW

Square T was translated by the rule (x + 2, y + 2) and then dilated from the origin by a scale factor of 3 to create square T″. Which statement explains why the squares are similar?

Translations and dilations preserve betweenness of points; therefore, the corresponding sides of squares T and T″ are proportional.