Pass Check: Similarity & Congruence
Congruent shapes are identical; similar shapes are the same shape but scaled.
Congruent
Shapes that are exactly the same size and shape - all sides and angles match.
Similar
Shapes with the same angles and sides in the same ratio, but different sizes.
Scale factor
The number you multiply lengths by to go from one similar shape to another.
SSS/SAS/ASA/RHS
The four congruence conditions: side-side-side, side-angle-side, angle-side-angle, right angle-hypotenuse-side.
Quick check
Mixed quiz
1. Prove triangles ABC and ADE are similar where DE is parallel to BC, both triangles sharing angle A. State the reason both share angle A and have equal corresponding angles.
2. Two triangles have all three pairs of sides equal in length. Which congruence condition is this?
3. Two right-angled triangles have equal hypotenuses and one equal other side. Which condition proves congruence?
4. Which of these is NOT a standard congruence condition for triangles?
5. Two triangles have two equal angles and one equal corresponding side (not between the angles). Which condition is this?
6. Prove two triangles congruent: both have a right angle, equal hypotenuse of 10cm, and one other equal side of 6cm. Which condition applies?
7. Two triangles have two equal sides and the included angle equal. Which condition is this?
8. Point A(2, 3) is translated by vector (3, -2). Find the coordinates of the image.