If triangle XYZ is similar to triangle ABC, what can we conclude about their perimeters?

The ratio of the perimeters of similar triangles is equal to the ratio of their corresponding sides. If $$\frac{XY}{AB} = k$$ , then $$\frac{Perimeter_{XYZ}}{Perimeter_{ABC}} = k$$ .

What is the formula for finding the length of a side in similar triangles?

If triangle ABC is similar to triangle DEF, and you know the lengths of some sides, you can use the formula: $$\frac{AB}{DE} = \frac{BC}{EF} = \frac{CA}{FD}$$ to find unknown lengths.

What is the relationship between the angles of similar quadrilaterals?

In similar quadrilaterals, corresponding angles are equal. For example, if quadrilateral ABCD is similar to quadrilateral EFGH, then angle A = angle E, angle B = angle F, etc.

How do you determine if two triangles are similar using side lengths?

You can use the SSS (Side-Side-Side) criterion, which states that if the lengths of the corresponding sides of two triangles are proportional, then the triangles are similar.

What is the relationship between the areas of similar figures?

The ratio of the areas of two similar figures is equal to the square of the ratio of their corresponding sides. If $$\frac{AB}{DE} = k$$ , then $$\frac{Area_{XYZ}}{Area_{ABC}} = k^2$$ .

What does it mean for two angles to be equal in similar triangles?

If two angles are equal in similar triangles, it confirms that the triangles are similar, as all corresponding angles must be equal.

How can you use corresponding sides to solve for unknown lengths?

You can set up a proportion using the lengths of the corresponding sides to solve for unknown lengths. For example, if $$\frac{AB}{DE} = \frac{BC}{EF}$$ , you can find the unknown side by cross-multiplying.

What is the importance of understanding corresponding sides and angles in geometry?

Understanding corresponding sides and angles is crucial for solving problems involving similar figures, as it allows for the application of proportional reasoning and the use of similarity criteria.

7M_5.1 Corresponding Sides and Angles

Flashcard

•

Mathematics

•

7th Grade

•

Practice Problem

•

Hard

•

CCSS

8.G.A.2, HSG.SRT.A.2, HSG.SRT.B.5

Standards-aligned

Wayground Content

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15 questions

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FLASHCARD QUESTION

Front

What are corresponding sides in similar triangles?

Back

Corresponding sides are the sides of two or more similar triangles that are in the same relative position. For example, if triangle ABC is similar to triangle DEF, then side AB corresponds to side DE.

Tags

CCSS.8.G.A.2

CCSS.HSG.CO.B.6

FLASHCARD QUESTION

Front

What are corresponding angles in similar triangles?

Back

Corresponding angles are the angles of two or more similar triangles that are in the same relative position. For example, if triangle ABC is similar to triangle DEF, then angle A corresponds to angle D.

Tags

CCSS.8.G.A.2

CCSS.HSG.CO.B.6

FLASHCARD QUESTION

Front

If triangle PQR is similar to triangle STU, what can we say about their angles?

Back

The corresponding angles of triangle PQR and triangle STU are equal, meaning @@ riangle PQR ext{ is similar to } riangle STU ext{ implies } ext{angle P} = ext{angle S}, ext{angle Q} = ext{angle T}, ext{angle R} = ext{angle U}.$$

Tags

CCSS.HSG.SRT.A.2

FLASHCARD QUESTION

Front

What is the relationship between the sides of similar triangles?

Back

Tags

CCSS.HSG.SRT.A.2

FLASHCARD QUESTION

Front

How do you identify corresponding sides in similar figures?

Back

To identify corresponding sides, look for the same position in each figure. For example, in triangles ABC and DEF, if A corresponds to D, then side AB corresponds to side DE.

Tags

CCSS.8.G.A.2

CCSS.HSG.CO.B.6

FLASHCARD QUESTION

Front

What does it mean for two shapes to be similar?

Back

Two shapes are similar if they have the same shape but not necessarily the same size. This means their corresponding angles are equal and their corresponding sides are in proportion.

Tags

CCSS.8.G.A.2

CCSS.HSG.CO.B.6

FLASHCARD QUESTION

Front

What is the significance of the AA criterion for similarity?

Back

The AA (Angle-Angle) criterion 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

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