1. Stating the problem for Day 4: Given quadrilateral ABEDC with triangles ABE and DEC, determine the nature of these triangles, show that angle AÊB = 70°, and deduce the measure of angle BÊC. 2. To determine the nature of triangles ABE and DEC, we use the properties of triangles and angle sum rules. 3. For triangle ABE, given angle at B is 40°, and assuming other angles or sides are known or can be deduced, use triangle angle sum property: $$\text{sum of angles} = 180^\circ$$. 4. For triangle DEC, analyze given angles and sides to classify the triangle (e.g., isosceles, right, equilateral) based on angle measures or side lengths. 5. To show that angle AÊB = 70°, use angle sum in triangle ABE: $$A\hat{E}B = 180^\circ - 40^\circ - \text{other angle}$$. Calculate accordingly. 6. To deduce angle BÊC, use properties of quadrilateral ABEDC and angle relationships, possibly supplementary or complementary angles. 1. Stating the problem for Day 5: Given an equilateral triangle ABC with side 4 cm, and right angles at ÊBC and FÊCB, reproduce the figure, prove (EB) is parallel to (FC), calculate angles ÂBE and ÂCF, calculate angles ÊAB and F̂AC, prove triangles ABE and ACF are equal and write homologous elements, and prove triangle AEF is equilateral. 2. Since ABC is equilateral, all sides are 4 cm and all angles are 60°. 3. To prove (EB) is parallel to (FC), use properties of right angles and corresponding angles formed by transversals. 4. Calculate angles ÂBE and ÂCF using triangle angle sum and given right angles. 5. Calculate angles ÊAB and F̂AC similarly. 6. To prove triangles ABE and ACF are equal, use criteria such as SAS or ASA by comparing sides and angles. 7. Write homologous elements by matching corresponding vertices and sides. 8. To prove triangle AEF is equilateral, show all sides are equal using previous results and properties of equilateral triangles. Final answers depend on detailed calculations and given data.