Practice Set 1.1 Geometry 10th Std Maths Part 2 Answers Chapter 1 Similarity
Question 1
Maharashtra Board Solution
Base of a triangle is 9 and height is 5. Base of another triangle is 10 and height is 6. Find the ratio of areas of these triangles.
Solution & Step-by-Step Answer:
Let the base, height and area of the first triangle be b1, h1, and A1 respectively. Let the base, height and area of the second triangle be b2, h2 and A2 respectively.
[Since Ratio of areas of two triangles is equal to the ratio of the product of their bases and corresponding heights]
∴ The ratio of areas of the triangles is 3:4.
Question 2
Maharashtra Board Solution
In the adjoining figure, BC ± AB, AD _L AB, BC = 4, AD = 8, then find
Solution & Step-by-Step Answer:
∆ABC and ∆ADB have same base AB. [Since Triangles having equal base]
Question 3
Maharashtra Board Solution
In the adjoining figure, seg PS ± seg RQ, seg QT ± seg PR. If RQ = 6, PS = 6 and PR = 12, then find QT.
Solution & Step-by-Step Answer:
In ∆PQR, PR is the base and QT is the corresponding height. Also, RQ is the base and PS is the corresponding height. [Ratio of areas of two triangles is equal to the ratio of the product of their bases and corresponding heights] ∴ ∴ PR × QT = RQ × PS ∴ 12 × QT = 6 × 6 ∴ QT = ∴ QT = 3 units
Question 4
Maharashtra Board Solution
In the adjoining figure, AP ⊥ BC, AD || BC, then find A(∆ABC) : A(∆BCD).
Solution & Step-by-Step Answer:
Draw DQ ⊥ BC, B-C-Q.
AD || BC [Given]
∴ AP = DQ (i) [Perpendicular distance between two parallel lines is the same]
∆ABC and ∆BCD have same base BC.
Question 5
Maharashtra Board Solution
In the adjoining figure, PQ ⊥ BC, AD ⊥ BC, then find following ratios.
Solution & Step-by-Step Answer:
i. ∆PQB and tPBC have same height PQ. ii. ∆PBC and ∆ABC have same base BC. iii. ∆ABC and ∆ADC have same height AD.
Question 1
Maharashtra Board Solution
Find
Solution & Step-by-Step Answer:
In ∆ABC, BC is the base and AR is the height. In ∆APQ, PQ is the base and AR is the height.