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6.03 Proving triangles similar

Interactive practice questions

This two-column proof shows that $\Delta ABC\sim\Delta XYZ$ΔABC~ΔXYZ in the attached diagram, but it is incomplete.

Statements Reasons
$\frac{AC}{XZ}=\frac{BC}{ZY}$ACXZ=BCZY Given
$\angle ACB\cong\angle XZY$ACBXZY

Given

$\Delta ABC\sim\Delta XYZ$ΔABC~ΔXYZ

$\left[\text{____}\right]$[____]

Select the correct reason to complete the proof.

Angle-angle similarity (AA$\sim$~)

A

Side-angle-side similarity (SAS$\sim$~)

B

Side-side-side similarity (SSS$\sim$~)

C

Angle-angle similarity (AA$\sim$~)

A

Side-angle-side similarity (SAS$\sim$~)

B

Side-side-side similarity (SSS$\sim$~)

C
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This two-column proof shows that two triangles in the attached diagram are similar, but it is incomplete.

This two-column proof shows that two triangles in the attached diagram are similar, but it is incomplete.

This two-column proof shows that two triangles in the attached diagram are similar, but it is incomplete.

Outcomes

GEO-G.SRT.5a

Use congruence and similarity criteria for triangles to solve problems algebraically and geometrically.

GEO-G.SRT.5b

Use congruence and similarity criteria for triangles to prove relationships in geometric figures.

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