1. **Problem 1.3:** Two similar triangles have areas 18 cm² and 32 cm². The base of the smaller triangle is 6 cm. Find the base of the larger triangle. 2. **Formula and rule:** For similar triangles, the ratio of their areas equals the square of the ratio of their corresponding sides: $$\frac{\text{Area}_1}{\text{Area}_2} = \left(\frac{\text{side}_1}{\text{side}_2}\right)^2$$ 3. **Apply the formula:** Let the base of the larger triangle be $x$ cm. $$\frac{18}{32} = \left(\frac{6}{x}\right)^2$$ 4. **Simplify the fraction:** $$\frac{9}{16} = \frac{36}{x^2}$$ 5. **Cross multiply:** $$9x^2 = 16 \times 36$$ 6. **Calculate right side:** $$9x^2 = 576$$ 7. **Divide both sides by 9:** $$\cancel{9}x^2 = \frac{576}{\cancel{9}}$$ $$x^2 = 64$$ 8. **Take square root:** $$x = \sqrt{64} = 8$$ 9. **Answer for 1.3:** The base of the larger triangle is 8 cm (Option D). --- 10. **Problem 1.4:** Identify the parallelogram with diagonals that bisect corner angles and bisect each other at right angles, but no interior angle is right angle. 11. **Explanation:** - A square has right angles, so not it. - A rectangle has right angles, so not it. - A rhombus has diagonals that bisect angles and intersect at right angles. - A general parallelogram does not have diagonals bisecting angles or intersecting at right angles. 12. **Answer for 1.4:** The figure is a Rhombus (Option B). --- 13. **Problem 1.10:** Triangle ABC is similar to triangle XYZ. Side XZ measures 10 units. Which concept is most appropriate to find the area of triangle XYZ? 14. **Explanation:** Similar triangles have proportional sides and areas related by the square of the scale factor. Proportionality is the key concept to relate sides and areas. 15. **Answer for 1.10:** Proportionality (Option B).