Geometry Past Papers PDF

## Page 1 If 150 cm², then complete the following activity to find A(AQOA). | | | |---|---| | 150 | A(AQOA) | | | 150 x | | | 5² | | A(AQOA) = | cm² | If the area of two similar triangles are equal, then prove that they are congruent. In the figure sides AB, BC, CA of ΔABC are produced upt...

## Page 1 If 150 cm², then complete the following activity to find A(AQOA). | | | |---|---| | 150 | A(AQOA) | | | 150 x | | | 5² | | A(AQOA) = | cm² | If the area of two similar triangles are equal, then prove that they are congruent. In the figure sides AB, BC, CA of ΔABC are produced upto points R, P, F respectively such that AB=BR, BC = CP and CA=AF. Prove that: A(APFR) = 7A(ΔABC) In ABCD, side BC || side AD. Diagonals AC and BD intersect each other at P. If AP= 1/2 AC, then prove that DP = 1/2 BP. In ΔPQR, seg XY || side QR. Points M and N are midpoints of seg PY and seg PR respectively. Prove that: a) ΔΡΧΜ ~ ΔΡΩΝ b) seg XM || seg QN. If ΔABC ~ ΔPQR, A(ΔABC) = 81 cm², A(APQR) = 121 cm², BC = 6.3 cm, then complete the following activity to find QR. | | | |---|---| | | (6.3)² | | | QR² | | | QR² | | | QR² | | QR = | cm | | QR = | cm | ## Page 2 1. In ΔABC, PQ is a line segment intersecting AB at P and AC at Q such that seg PQ || seg BC. If PQ divides ΔABC into two equal parts having equal areas, find BP/AB. 2. In the figure, D is point on BC such that ∠ABD = ∠CAD. If AB=5 cm, AD = 4 cm and AC = 3 cm. Find: i) BC ii) DC iii) A(ACD): A(ABCA) 3. In the figure, seg DH ⊥ side EF and seg GK ⊥ side EF. If DH = 12 cm, GK = 20 cm and A(ADEF) = 300 cm². Find: i) EF ii) A(GEF) iii) A(DEGF) 4. The sides of the smaller triangle, out of the two similar triangles are 4 cm, 5 cm, 6 cm respectively. If the perimeter of the larger triangle is 90 cm, then what are the lengths of the sides of the larger triangle? 5. In ΔABC, AD is the bisector of ∠BAC. Seg AL ⊥ side BC. Prove that A(ΔABD)/A(ACD) = AB/AC by completing the following activity: In ΔABD, seg AD is the bisector of ∠BAC. ... by theorem of an angle bisector of a triangle. ΔABC and AADC have same height ... [from (1) and (2) ] 6. In the figure, PB and QA are perpendiculars to seg AB. If PO = 5 cm, QO = 7 cm and A(ΔΡΟΒ) ## Page 3 4. ΔPQR ~ AXYZ. Write the proportionality of its corresponding sides. 5. IF ΔABC~ ΔLMN and ∠A = 60°, then what will be the measure of ∠L? State your reason. 6. Observe the figure and state whether AABC is similar to APQR or not? Why? 6. In the figure, line PQ || side BC, AP = 2.4 cm, PB = 7.2 cm, QC = 5.4 cm, then find AQ. 7. In ΔPQR, NM || RQ. If PM = 15, MQ = 10, NR=8, then find PN. 8. In the figure, seg AB ⊥ seg BC and seg DC ⊥ seg BC. If AB=3 cm and CD=4 cm, then find A(ΔABC) 9. If ΔABC~APQR and A(ΔABC)/A(APQR) = 16/25, then find AB: PQ. ## Page 4 1. ΔABC ~ ΔPQR. A(ΔABC) = 81 cm², A(APQR) = 121 cm². If BC = 6.3 cm, then find QR. 2. In ΔPQR, ray PS is the bisector of ∠QPR. Q-S-R. If QS = 4.8 cm, SR = 3.6 cm, then find PQ : PR. 3. IF ΔABC ~ AEDC, AC = 15, BC = 10, CE = 12, then find CD. 4. In ΔABC ~ ΔPQR, AB: PQ = 4:5 and A(APQR) = 125 cm², then find A(AABC). 5. The ratio of the areas of two triangles A₁: A₂ is 3: 2. The corresponding bases are b₁ and b₂. The heights of the triangles are equal. If b₂ = 12 cm. Find b₁. 6. In the figure, for what value of r will seg DE be parallel to BC? 7. A vertical pole 40 m long casts a shadow 20 m long on the ground. At the same time, a ...... high tower casts a shadow 50 m long on the ground.. 8. Sides of two similar triangles are in the ratio 3: 5. Areas of these triangles are in the ratio 9. The areas of two similar triangles are 36 cm² and 121 cm². The ratio of their corresponding sides is 10. In the figure, ∠AED = ∠ABC, AD = 3, DB = 5, AE = 4, then length of AC is 11. ΔPQR ~ ASTU and A(APQR): A(ASTU) = 64: 81, then what is the ratio of corresponding sides? 12. Which of the following is not the test of similarity? 13. The corresponding medians of two similar triangles are in the ratio 4: 7. Let their respective areas be A, and A2. A: A2= 14. In the figure, line AD || line BE || line CF. AB = 8, BC = 4, DE = 6, then EF = ? 15. If ΔABC ~ APQR and 4A(ABC)=25A(APQR), then AB: PQ = ? 16. ΔABC ~ APQR. If AB = 4 cm, PQ = 6 cm and QR = 9 cm, then BC = ....... 17. If AABC~ △DEF and ∠A = 48°, then ∠D= ## Page 5 1. In the figure, line PQ || side BC. Write the ratio in which sides AB and AC are divided proportionately. Also give your reason. 2. Observe the figure and state with reason whether line XY || side BC or not. 3. In the figure, line AX || line BY || line CZ. Complete the following ratio : AB/YZ 1. ΔABC ~ △DEF, then AB/DE = EF/____ 2. In the figure, BD = 8, BC = 12 and B-D-C, then A(ΔABD)/A(ΔADC) 3. In the figure, ray QS is the bisector of ∠PQR and PQ = QR, then PS/SR =