Determine whether two triangles are similar

Similar triangles have the same shape, but not necessarily the same size

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Views #: 240

Questions #: 10

Time: 10 minutes

Pass Score: 80.0%

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Similar vs. Congruent – What Is the Difference?

1 pts

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Two triangles are similar when they have the same shape but not necessarily the same size. Study the pair below:

Which statement about similar triangles is always true?

Corresponding sides are equal in length.

Corresponding angles are congruent and corresponding sides are proportional.

The triangles must be the same size.

Similar triangles are never congruent.

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Explanation

The AAA Similarity Theorem

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What does the AAA Similarity Theorem state?

If three sides of one triangle equal three sides of another, the triangles are similar.

If the angles of one triangle are congruent to corresponding angles of another triangle, the triangles are similar.

If two sides and the included angle are congruent, the triangles are similar.

All triangles with the same perimeter are similar.

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Corresponding Angles of Similar Triangles

1 pts

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Given that \(\triangle PQR \sim \triangle CDE\), which three pairs of angles are congruent?

\(\angle P \cong \angle C,\; \angle Q \cong \angle D,\; \angle R \cong \angle E\)dummy

\(\angle P \cong \angle D,\; \angle Q \cong \angle C,\; \angle R \cong \angle E\)dummy

\(\angle P \cong \angle E,\; \angle Q \cong \angle D,\; \angle R \cong \angle C\)dummy

\(\angle P \cong \angle C,\; \angle Q \cong \angle E,\; \angle R \cong \angle D\)dummy

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Proportional Sides of Similar Triangles

2 pts

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Given \(\triangle PQR \sim \triangle CDE\), complete the compact proportion of all three pairs of corresponding sides:

\(\dfrac{PQ}{\Box} = \dfrac{QR}{\Box} = \dfrac{PR}{\Box}\)

Side \(PQ \cong\) = (1)
Side \(QR \cong\) = (2)
Side \(PR \cong\) = (3)

Please drag and drop the selected option in the right place or type it instead

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Parallel Lines and Similar Triangles

2 pts

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In the figure below, \(\overline{PR} \parallel \overline{MN}\). Are \(\triangle PQR\) and \(\triangle NQM\) similar triangles?

Yes — by the AAA similarity theorem, since vertical angles and alternate interior angles are congruent.

No — parallel lines do not create similar triangles.

Yes — but only because the triangles share vertex Q.

Cannot be determined without knowing the side lengths.

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Find the Unknown Side – Similar Triangles

2 pts

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In the figure below, \(\triangle RST \sim \triangle JKL\). Find \(x\).

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Find a Second Unknown Side – Same Similar Triangles

2 pts

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Using the same pair \(\triangle RST \sim \triangle JKL\) (where \(RT = 48\), \(JL = 32\), \(RS = 36\)), find \(y = JK\).

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Select All True Statements About Similar Triangles

2 pts

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Select all statements that are true.

Congruent triangles are always similar.

Similar triangles are always congruent.

If two triangles are similar, their corresponding angles are congruent.

If two triangles are similar, their corresponding sides are proportional.

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Classify Corresponding Angles

2 pts

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Angle Pairs

×\(\angle G\) and \(\angle I\)

×\(\angle E\) and \(\angle J\)

×\(\angle F\) and \(\angle H\)

×\(\angle G\) and \(\angle J\)

Congruent (Corresponding)

NOT Corresponding

Given that \(\triangle GEF \sim \triangle IJH\), drag each angle pair into the correct category.

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Find the Unknown in △DEF ∼ △GHI

2 pts

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In the figure, \(\triangle DEF \sim \triangle GHI\). Given \(DE = 4.5\), \(GH = 9\), and \(EF = 13.5\), find \(y = HI\).

25.5

28.5

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Year 9

Similar vs. Congruent – What Is the Difference?

Correct Answer

Explanation

The AAA Similarity Theorem

Correct Answer

Explanation

Corresponding Angles of Similar Triangles

Correct Answer

Explanation

Proportional Sides of Similar Triangles

Correct Answer

Explanation

Parallel Lines and Similar Triangles

Correct Answer

Explanation

Find the Unknown Side – Similar Triangles

Correct Answer

Explanation

Find a Second Unknown Side – Same Similar Triangles

Correct Answer

Explanation

Select All True Statements About Similar Triangles

Correct Answer

Explanation

Classify Corresponding Angles

Correct Answer

Explanation

Find the Unknown in △DEF ∼ △GHI

Correct Answer

Explanation

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