Back to Exercise: Explain similarity transformations

Exercises: Define Similarity Using Transformations

Work through each section in order. Show your reasoning where indicated.
For problems involving figures, identify corresponding parts before checking ratios or angles.

Grade 9·21 problems·~28 min·Common Core Math - HS Geometry·standard·hsg-srt-a-2

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Warm-Up: Review What You Know

These problems review skills from earlier lessons.

A dilation centered at the origin maps triangle $ABC$ onto triangle $A'B'C'$ with scale factor $k = 3$ . If $AB = 5$ , what is $A'B'$ ?

Two figures are congruent. Which type of transformation sequence maps one onto the other?

A dilation only

A sequence of rigid motions only (translations, rotations, reflections)

A dilation followed by a rigid motion

Any combination of dilations and rigid motions

A dilation with scale factor $k$ is applied to a triangle. Which property is preserved (unchanged) by the dilation?

Side lengths

Angle measures

Perimeter

Area

Fluency Practice

A similarity transformation is defined as which sequence of transformations?

One or more dilations only

One or more rigid motions only

Zero or more rigid motions followed by a dilation

A dilation followed by zero or more rigid motions, but never a dilation alone

Triangle $PQR$ is similar to triangle $STU$ with scale factor $k = 2.5$ . If $PQ = 8$ , what is the length of $ST$ ?

$Two right triangles: triangle ABC with sides 6, 8, 10 and triangle DEF with sides 9, 12, 15$

Triangle $ABC$ has sides $AB = 6$ , $BC = 8$ , $CA = 10$ . Triangle $DEF$ has sides $DE = 9$ , $EF = 12$ , $FD = 15$ . Are the triangles similar?

Yes — all three pairs of corresponding sides are proportional with $k = 1.5$

No — the triangles are different sizes, so they cannot be similar

Yes — but only because they are right triangles

Cannot be determined without knowing the angle measures

$Two rectangles: ABCD with dimensions 4 by 10, and EFGH with dimensions 6 by 15$

Rectangle $ABCD$ has dimensions $4 \times 10$ . Rectangle $EFGH$ has dimensions $6 \times 15$ . What is the scale factor $k$ from $ABCD$ to $EFGH$ ?

Triangle $JKL \sim$ triangle $MNP$ with scale factor $k = 3$ . If $\angle J = 47^\circ$ and $\angle K = 68^\circ$ , what is $\angle N$ ?

$47^\circ$

$65^\circ$

$68^\circ$

$204^\circ$

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