This document contains 10 geometry problems involving properties of triangles, parallelograms, midpoints and ratios of lengths and areas. The problems can be solved using definitions of special line segments and angles in various shapes including triangles, trapezoids and parallelograms.

2. 1) IN THE GIVEN FIGURE, DE IS PARALLEL TO BC AND D
AND E ARE THE MID POINTS OF SIDES AB AND AC
RESPECTIVELY.
The ratio of the lengths of DE and BC is:
A) 1/2
B) 1
C)3/2
D) 2

3. 2) IN THE GIVEN FIGURE, D AND E ARE POINTS ON SIDES AC
AND BC OF ΔABC SUCH THAT AD = DC AND BE = EC.
What is the measure of ∠B?
A) 50°
B) 60°
C) 70°
D) 80°

4. 3) PQRS BISECT EACH OTHER AT O. A, B, AND C ARE THE
MID-POINTS OF OP, PS, AND OS RESPECTIVELY.
If ΔABC is right-angled at B, where AB = BC = 5 cm, then what
is the area of the quadrilateral PQRS?
A) 30 cm2
B) 60 cm2
C) 200cm2
D) 400cm2

5. 4) THE GIVEN FIGURE SHOWS A TRIANGLE ABC IN WHICH
D, E, AND F ARE THE MID-POINTS OF SIDES AB, BC, AND
CA RESPECTIVELY.
If the area of ΔABC is 272 m2, then what is the area of
ΔDEF?
A) 204m²
B) 136m²
C) 84m²
D) 68m²

6. 5) IN THE GIVEN FIGURE, ABCD IS A TRAPEZIUM WHERE AB ||
DC.
E IS THE MID POINT OF AD. FROM E, A LINE IS DRAWN
PARALLEL TO AB INTERSECTING BC AT F.
What is the measure of FC, if BC = 8 cm?
A) 2cm
B) 4cm
C) 6cm
D) 8cm

7. 6) IN THE TRIANGLE ABC SHOWN IN THE ADJACENT
FIGURE, AD IS THE MEDIAN THROUGH A AND E IS THE
MID POINT OF AD. BE PRODUCED MEETS AC IN F. THE
LENGTHS AB, BC, AC AND AF ARE INTEGERS.
The length of the side AF can be
A) 6
B) 8
C) 10
D) 11

8. 7) IN PARALLELOGRAM PQRS, THE VERTICES ARE TAKEN IN
ORDER. IF ∠P:∠Q = 7:3, THEN WHAT IS THE MEASURE
OF ∠R?
A) 126°
B) 116°
C) 64°
D) 54°

9. 8) IN A PARALLELOGRAM PQRS, WHERE VERTICES ARE
TAKEN IN ORDER; ∠P = 60°, THEN WHAT ARE THE
RESPECTIVE MEASURES OF ∠Q AND ∠R?
A) 60° and 120°
B) 60° and 60°
C) 120° and 120°
D) 120° and 60°

10. 9) IN THE GIVEN FIGURE, AE = EB = AF = 2 CM AND
BCDE IS A PARALLELOGRAM.
What is the length of FC?
A) 1 cm
B) 2cm
C) 3 cm
D) 4 cm

11. 10) THE DIAGONALS AC AND BD OF PARALLELOGRAM
ABCD INTERSECT AT O. WHAT IS THE RATIO OF THE
AREA OF PARALLELOGRAM ABCD AND ΔAOB?
A) 1: 1
B) 2: 1
C) 3: 1
D) 4: 1