Calculate the size of B with reasons. 5.1.2. Classify triangle ABD. 5.2.1. Identify whether the two triangles are congruent or similar. 5.2.2. Describe the properties that make them congruent or similar. 5.3. ABCD is a rhombus. Determine, with reasons, the size of :

5.1.1 Calculate the size of $\hat{B}$ with reasons.

5.1.2 Classify $\triangle ABD$. $\triangle ABD$ is a right-angled triangle.

5.2.1 Identify whether the two triangles are congruent or similar. To check for similarity, we compare the ratios of corresponding sides: $\frac{DE}{AC} = \frac{10}{5} = 2$ $\frac{DF}{AB} = \frac{14}{7} = 2$ $\frac{EF}{BC} = \frac{18}{9} = 2$ Since the ratios of all corresponding sides are equal, the triangles are similar.

5.2.2 Describe the properties that make them congruent or similar. The properties that make them similar are:

• Their corresponding angles are equal.
• Their corresponding sides are in proportion.

5.3 ABCD is a rhombus. Determine, with reasons, the size of:

• Angle 1 ($\angle AOB$) Step 1: Identify the property of diagonals in a rhombus. The diagonals of a rhombus bisect each other at right angles. Step 2: State the angle. $\angle AOB = \boxed{\text{90}^\circ}$ Reason: Diagonals of a rhombus intersect at right angles.

• Angle 2 ($\angle ADO$) Step 1: Use the properties of a rhombus and sum of angles in a triangle. In $\triangle AOD$: $\angle DAO = 22^\circ$ (Given) $\angle AOD = 90^\circ$ (Diagonals of a rhombus intersect at right angles) Step 2: Calculate $\angle ADO$. $\angle ADO = 180^\circ - \angle DAO - \angle AOD$ (Sum of angles in a triangle) $\angle ADO = 180^\circ - 22^\circ - 90^\circ$ $\angle ADO = \boxed{\text{68}^\circ}$ Reason: Sum of angles in a triangle.