#### Geometry Two Marks Questions

8th Standard EM

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Maths

Time : 00:45:00 Hrs
Total Marks : 30
15 x 2 = 30
1. In the given fi gure YH||TE . Prove that ΔWHY～ΔWET and also fi nd HE and TE.

2. In the given fi gure, ∠CIP≡∠COP and ∠HIP≡∠HOP . Prove that IP ≡ OP.

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

4. In the given figure, find PT given that l1|| l2.

5. In the figure, given that ∠1 =∠2 and ∠3 ≡∠4. Prove that ΔMUG ≡ ΔTUB.

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

7. In the figure, PQ ≡ TS, Q is midpoint of PR, S is the midpoint TR and ∠PQU≡∠TSU. Prove that QU ≡ SU.

8. 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.

9. Construct the following quadrilaterals with the given measurements and also find their area.
PLAY, PL= 7 cm, LA = 6 cm, AY= 6 cm, PA = 8 cm and LY = 7 cm.

10. Construct the following quadrilaterals with the given measurements and also find their area.
AGRI, AG= 4.5 cm, GR = 3.8 cm, ∠A = 60°, ∠G = 110° and ∠R = 90°.

11. 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°.

12. Fill in the blanks with the correct term from the given list.
(in proportion, similar, corresponding, congruent shape, area, equal)
(i) Corresponding sides of similar triangles are _______.
(ii) Similar triangles have the same _________ but not necessarily the same size.
(iii) In similar triangles, ______ sides are opposite to equal angles.
(iv) The symbol ≡ is used to represent _______ triangles.
(v) The symbol ～ is used to represent ________ triangles

13. Is it possible to construct a quadrilateral PQRS with PQ = 5 cm, QR = 3 cm, RS = 6 cm, PS = 7 cm and PR = 10 cm. If not, why?

14. In the figure AB$\bot$ BC and DE$\bot$AC prove that $\triangle$ABC ~$\triangle$AED.

15. In the given figure if $\angle$P =$\angle$RTS, prove that $\triangle$RPQ ~$\triangle$ RTS.