Triangle Similarity

Front

What is Triangle Similarity?

Back

Triangle similarity refers to the condition where two triangles have the same shape but may differ in size. This means that their corresponding angles are equal and their corresponding sides are in proportion.

Tags

CCSS.8.G.A.2

CCSS.HSG.CO.B.6

Front

What does SSS Similarity stand for?

Back

SSS Similarity stands for 'Side-Side-Side' similarity, which states that if the three sides of one triangle are proportional to the three sides of another triangle, then the triangles are similar.

Tags

CCSS.HSG.SRT.B.5

Front

What does AA Similarity stand for?

Back

AA Similarity stands for 'Angle-Angle' similarity, which states that if two angles of one triangle are equal to two angles of another triangle, then the triangles are similar.

Tags

CCSS.HSG.SRT.A.2

Front

What does SAS Similarity stand for?

Back

SAS Similarity stands for 'Side-Angle-Side' similarity, which states that if two sides of one triangle are proportional to two sides of another triangle and the included angles are equal, then the triangles are similar.

Tags

CCSS.HSG.SRT.B.5

Front

How can you determine if two triangles are similar using the AA criterion?

Back

To determine if two triangles are similar using the AA criterion, check if two angles of one triangle are equal to two angles of the other triangle. If they are, the triangles are similar.

Tags

CCSS.HSG.SRT.A.2

Front

What is the significance of corresponding angles in similar triangles?

Back

In similar triangles, corresponding angles are equal. This property is crucial for establishing triangle similarity using the AA criterion.

Tags

CCSS.HSG.SRT.A.2

Front

What is the significance of corresponding sides in similar triangles?

Back

In similar triangles, corresponding sides are in proportion. This means that the ratio of the lengths of corresponding sides is constant.

Tags

CCSS.HSG.SRT.A.2

Front

Can two triangles be similar if only one pair of angles is equal?

Back

No, two triangles cannot be similar if only one pair of angles is equal. At least two pairs of angles must be equal for the triangles to be similar (AA criterion).

Tags

CCSS.HSG.SRT.A.2

Front

What is the relationship between the areas of similar triangles?

Back

The areas of similar triangles are proportional to the square of the lengths of their corresponding sides. If the ratio of the sides is k, then the ratio of the areas is k².

Front

How do you apply the SSS similarity criterion in practice?

Back

To apply the SSS similarity criterion, measure the lengths of the sides of both triangles and check if the ratios of the corresponding sides are equal.

Tags

CCSS.HSG.SRT.B.5