Year 9 Maths: Congruence & Similarity PDF

Topic: Congruence and Similarity Topic/Skill Definition/Tips Example 1. Congruent Shapes are congruent if they are identical - Shapes same shape and same size. Shapes can be rotated or reflected but still be c...

Topic: Congruence and Similarity Topic/Skill Definition/Tips Example 1. Congruent Shapes are congruent if they are identical - Shapes same shape and same size. Shapes can be rotated or reflected but still be congruent. 2. Congruent 4 ways of proving that two triangles are Triangles congruent: 1. SSS (Side, Side, Side) 2. RHS (Right angle, Hypotenuse, Side) 3. SAS (Side, Angle, Side) 4. ASA (Angle, Side, Angle) or AAS ASS does not prove congruency. 3. Similar Shapes are similar if they are the same Shapes shape but different sizes. The proportion of the matching sides must be the same, meaning the ratios of corresponding sides are all equal. 4. Scale Factor The ratio of corresponding sides of two similar shapes. To find a scale factor, divide a length on one shape by the corresponding length on a similar shape. Scale Factor = 15 ÷ 10 = 1.5 5. Finding 1. Find the scale factor. missing 2. Multiply or divide the corresponding lengths in side to find a missing length. similar shapes If you are finding a missing length on the larger shape you will need to multiply by the scale factor. If you are finding a missing length on the smaller shape you will need to divide by Scale Factor = 3 ÷ 2 = 1.5 the scale factor. 𝑥 = 4.5 × 1.5 = 6.75𝑐𝑚 6. Similar To show that two triangles are similar, Triangles show that: 1. The three sides are in the same proportion 2. Two sides are in the same proportion, and their included angle is the same 3. The three angles are equal