unit 2

1. Congruent figures

1.1. Congruent figures are identical figures; that is, they have the same shape and size.

1.1.1. New node

1.2. When stating one figure is congruent to another, the vertices should be listed in corresponding (or matching) order

2. Triangle constructions

2.1. If two angles of a triangle and the side between them, or two sides and an angle between them are known, the triangle can be constructed using a protractor and a ruler. When using a protractor: make sure that the baseline of the protractor is exactly on the line, and the cross of the protractor is exactly on the point from which you are measuring the angle. use the scale that begins from 0° (not 180°). node

2.2. make sure that the baseline of the protractor is exactly on the line, and the cross of the protractor is exactly on the point from which you are measuring the angle. use the scale that begins from 0° (not 180°). node

2.3. A triangle can be constructed using a ruler and a pair of compasses if the three sides are known.

3. Quadrilaterals

3.1. A quadrilateral is a four-sided figure.

3.2. Opposite angles do not have rays in common.

3.3. Opposite sides do not intersect.

3.4. Diagonals connect opposite angles.

3.5. In some quadrilaterals, the diagonals bisect each other.

3.6. In some quadrilaterals, the diagonals bisect angles.

3.7. A parallelogram is a quadrilateral where the opposite sides are parallel.

3.8. A rhombus is a parallelogram in which all sides are congruent. (Because it is a parallelogram, the properties of a parallelogram are also properties of a rhombus.)

3.9. A rectangle is a parallelogram in which all angles are 90°. (Because it is a parallelogram, the properties of a parallelogram are also properties of a rectangle.)

3.10. A square is a rectangle with all sides congruent. (Because rectangles are parallelograms and a rhombus is a parallelogram with all sides congruent, a square is also a right-angled rhombus.)

3.11. A kite is a quadrilateral in which adjacent pairs of sides are congruent.

3.12. Congruent triangles can be used to investigate the properties of quadrilaterals.

3.13. Angles and parallel lines can be used to establish congruency in parallelograms.

4. Congruent triangles

4.1. Triangles are congruent if any one of the following applies.

4.2. Corresponding sides are the same (SSS).

4.3. Two corresponding sides and the included angle are the same (SAS).

4.4. Two angles and a pair of corresponding sides are the same (ASA).

4.5. The hypotenuse and one pair of the other corresponding sides are the same in a right-angled triangle (RHS).

4.6. The following do not show congruence.

4.7. Three corresponding angles are the same.

4.8. Two corresponding sides and a non-included angle are the same