4.8

Similarity and congruence

9 flashcards to master Similarity and congruence

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Definition Flip

Define 'similar' in the context of geometric shapes.

Answer Flip

Shapes are similar if they have the same angles and their corresponding sides are in proportion (equal ratios). One shape is an enlargement or reduction of the other, maintaining the same overall form.

Definition Flip

What does it mean for two triangles to be 'congruent'?

Answer Flip

Two triangles are congruent if they are exactly the same. This means all corresponding sides and angles are equal. There are four congruence tests: SSS, SAS, ASA, RHS.

Key Concept Flip

Triangle ABC has sides 3cm, 4cm, and 5cm. Triangle XYZ has sides 6cm, 8cm, and 10cm. Are they similar? Explain.

Answer Flip

Yes, they are similar. The sides are in the ratio 3:6, 4:8, and 5:10, which simplifies to 1:2. Since all corresponding sides are in the same ratio, the triangles are similar.

Definition Flip

State the condition for Side-Angle-Side (SAS) congruence.

Answer Flip

Two triangles are congruent by SAS if two sides and the included angle (the angle between those two sides) of one triangle are equal to the corresponding two sides and included angle of the other triangle.

Key Concept Flip

A rectangle has sides of length 2 and 5. A similar rectangle has a corresponding side of length 10. What is the length of the other side of the larger rectangle?

Answer Flip

The scale factor is 10/2 = 5. Therefore, the other side length is 5 * 5 = 25.

Key Concept Flip

The area scale factor between two similar figures is 9. What is the length scale factor?

Answer Flip

The area scale factor is the square of the length scale factor. Therefore, the length scale factor is the square root of 9, which is 3.

Key Concept Flip

The volume scale factor between two similar solids is 8. What is the length scale factor?

Answer Flip

The volume scale factor is the cube of the length scale factor. Therefore, the length scale factor is the cube root of 8, which is 2.

Key Concept Flip

Shapes A and B are similar. The ratio of their corresponding sides is 3:4. If the area of Shape A is 45 cm², what is the area of Shape B?

Answer Flip

The area scale factor is (4/3)² = 16/9. Area of Shape B = (16/9) * 45 cm² = 80 cm².

Key Concept Flip

Explain the difference between similarity and congruence.

Answer Flip

Similar shapes have the same angles and proportional sides (equal ratios), so one is an enlargement of the other. Congruent shapes are exactly identical; they have the same angles and the same side lengths.

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4.7 Circle theorems 4.9 Constructions and loci

Key Questions: Similarity and congruence

Define 'similar' in the context of geometric shapes.

Shapes are similar if they have the same angles and their corresponding sides are in proportion (equal ratios). One shape is an enlargement or reduction of the other, maintaining the same overall form.

What does it mean for two triangles to be 'congruent'?

Two triangles are congruent if they are exactly the same. This means all corresponding sides and angles are equal. There are four congruence tests: SSS, SAS, ASA, RHS.

State the condition for Side-Angle-Side (SAS) congruence.

Two triangles are congruent by SAS if two sides and the included angle (the angle between those two sides) of one triangle are equal to the corresponding two sides and included angle of the other triangle.

About Similarity and congruence (4.8)

These 9 flashcards cover everything you need to know about Similarity and congruence for your Cambridge IGCSE Mathematics (0580) exam. Each card is designed based on the official syllabus requirements.

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