#### Geometry Important Questions

8th Standard EM

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Maths

Time : 01:00:00 Hrs
Total Marks : 50
4 x 1 = 4
1. Two similar triangles will always have ________angles

(a)

acute

(b)

obtuse

(c)

right

(d)

matching

2. If in triangles PQR and XYZ, $\frac{PQ}{XY}=\frac{QR}{ZX}$ then they will be similar if

(a)

∠Q=∠Y

(b)

∠P=∠X

(c)

∠Q=∠X

(d)

∠P≡∠Z

3. If ΔABC～ΔPQR in which ∠A = 53o and ∠Q = 77o, then R is

(a)

50°

(b)

50°

(c)

70°

(d)

80°

4. In the figure, which of the following statements is true?

(a)

AB = BD

(b)

BD < CD

(c)

AC = CD

(d)

BC = CD

5. 9 x 2 = 18
6. In the given fi gure prove that ΔGUM ～ ΔBOX

7. In the given fi gure, if ΔEAT～ΔBUN, find the measure of all angles.

8. In the given fi gure, DBCD is isosceles with base BD and ∠BAE≡∠DEA Prove that AB ≡ ED.

9. In the given figure, D is the midpoint of OE and ∠CDE = 90°. Prove that ΔODC ≡ΔEDC

10. In the figure, ∠TEN≡∠TON=90o and TO ≡ TE. Prove that ∠ORN≡∠ERN.

11. Construct the following quadrilaterals with the given measurements and also find their area.
KITE, KI= 5.4 cm, IT = 4.6 cm, TE= 4.5 cm, KE = 4.8 cm and IE = 6 cm.

12. Construct the following quadrilaterals with the given measurements and also find their area.
PQRS, PQ=QR= 3.5 cm, RS= 5.2 cm, SP = 5.3 cm and ∠Q =120o.

13. Construct the following quadrilaterals with the given measurements and also find their area.
MIND, MI =3.6 cm, ND = 4 cm, MD= 4 cm, ∠M = 50° and ∠D = 100°.

14. Construct the following quadrilaterals with the given measurements and also find their area.
YOGA, YO = 6 cm, OG = 6 cm, ∠O = 55°, ∠G = 35° and ∠A = 100°.

15. 6 x 3 = 18
16. If PQ || RS and ∠ONR=30o find ∠MON and hence ∠MOX .

17. Find the unknowns in the following figures

18. Find the unknowns in the following figures

19. (Illustrating SAS Similarity)
If A is the midpoint of RU and T is the midpoint of RN, prove that ΔRAT ～ ΔRUN .

20. (Illustrating AAS and ASA Congruence)
If ∠YTB ≡∠YBT and ∠BOY≡∠TRY, prove that Δ BOY ≡ Δ TRY

21. (Illustrating RHS Congruence)
If TAP is an isosceles triangle with TA = TP and ∠TSA = 90°
Is ∠P = ∠A? Why?

22. 2 x 5 = 10
23. Construct a quadrilateral DEAR with DE = 6 cm, EA = 5 cm, AR = 5.5cm, RD = 5.2 cm and DA = 10 cm. Also find its area.

24. Construct a quadrilateral MATH with MA=4 cm, AT= 3.6 cm, TH = 4.5 cm, MH = 5 cm and ∠A = 85°. Also find its area.