New Trend Mathematics(2Nd Edition)S3A - Chapter Quiz - Chapter 5

New Trend Mathematics(2nd Edition)S3A - Chapter Quiz - Chapter 5

Theorems Related to Triangles

[Time allowed: 35 minutes]

1. In the figure, ADB, AEC, BFE and CFD are straight lines. BE and DC are the angle bisectors of ÐABC and ÐACB respectively. Ifand, find ÐACD.

(12 marks)

2. In the figure, BDC is a straight line. AD is a median of DABC,. If and, find the length of AD. (Give your answer correct to 3 significant figures.)

(13 marks)

3. In the figure, ADC is a straight line.,and. Prove that DABD is an isosceles triangle. (10 marks)

4. In the figure, ADB, AEC, DFC and EFB are straight lines. CD is the angle bisector of ÐACB. If,and, prove that BE is an altitude of DABC. (14 marks)

5. In the figure, AD is the perpendicular bisector of BC.and the perimeter of DABC is 30cm.

(a) Prove that. (5 marks)

(b) Find the length of AC. (4 marks)

6. (a) In the figure, find ÐACB. (4 marks)

(b) Write down the longest side and the shortest side of DABC as shown above. (8 marks)

7. In the figure, ABC is an isosceles triangle, where. O is the incentre of DABC. If, find ÐBOC. (16 marks)

8. In the figure, P, Q and R are the mid-points of AB, BC and AC respectively. O is the circumcentre of DABC. Ifand, find ÐPOR. (12 marks)

－End of Paper－

Solution

1. In DABC,

(angle bisector) 2M

\ (Ð sum of D) 2M

(angle bisector) 2M

2. In DABC,

(median) 2M

Let.

(Pyth. theorem) 2M

Let.

In DABD,

(Pyth. theorem) 2M

(corr. to 3 sig. fig.)

\ 1A

3. (ext. Ð of D) 2M

 2M

\ (sides opp. eq. Ðs) 2M

\ DABD is an isosceles triangle. 2

4. In DACD,

(Ð sum of D) 2M

(angle bisector) 2M

In DBEC,

(Ð sum of D) 2M

\ BE is an altitude of DABC. 2

5. (a) In DABD and DACD,

(common side) 1M

(perpendicular bisector) 1M

\ (S.A.S.) 1M

\ (corr. sides, @Ds) 1

(b) (given)

(proved)

\ DABC is an equilateral triangle. 2M

 The perimeter of DABC is 30cm.

\ 1M

\ 2A

6. (a) (Ð sum of D) 2M

(b)  2M

\ (greater Ð, greater side) 2M

\ BC and AC are the longest side and shortest side of DABC respectively. 4A

7. (base Ðs, isos. D) 2M

In DABC,

(Ð sum of D) 2M

 O is the incentre of DABC.

\ OB and OC are the angle bisectors of ÐABC and ÐACB respectively.

(angle bisector) 1M

In DOBC,

(Ð sum of D) 2M

8.  O is the circumcentre of DABC, P, Q and R are the mid-points of AB, BC and AC respectively.

\ OP, OQ and OR are the perpendicular bisectors of AB, BC and AC respectively.

\ 2M

(Ð sum of polygon) 2M

(Ðs at a pt.) 2M