# Tests for Congruency of Triangles

## Trending Questions

**Q.**

If two figures have same area, they must be

Congruent

Having equal sides

Similar

None of the above

**Q.**D is the mid point of side BC of triangle ABC and E is the mid point of BD. If O is the mid point of AE, then area of triangle BOE = 1/8 area of triangleABC

**Q.**In triangle ABC , D is the midpoint of AB. P IS ANY POINT OF BC. CQ || PD meets AB in Q . Show that ar ( ∆BPQ) = ½(∆ABC)

**Q.**In ∆ABC, AD is the median and P is any point on AD such that AP:PD=1:3. Find the area of ∆ABP.

**Q.**

In a triangle ABC, E is the mid-point of median AD.Then, ar (ΔBED) = 14ar(ΔABC)

14ar(ΔABD)

14ar(ΔABC)

14ar(ΔBCD)

14ar(ΔACB)

**Q.**

In ∆ABC, E is the mid-point of median AD. Area(∆BED)=

**Q.**Question 1

In the figure, PSDA is a parallelogram. Points Q and R are taken on PS such that PQ = RS and PA || QB || RC. Prove that ar (PQE) = ar (CFD).

**Q.**

AE is a median to side BC of triangle ABC. If area(∆ABC) = 24 cm, then area(∆ABE) =

16 cm

18 cm

8 cm

12 cm

**Q.**

ABCD is a quadrilateral whose diagonal AC divides it into two parts, equal in area, then ABCD cannot be

Parallelogram

Trapezium

Rectangle

Rhombus

**Q.**

ABC is a triangle in which D, E, F are the mid-points of BC, AC and AB respectively. If Area (ΔABC) = 32 cm^{2}, then Area of trapezium BFEC is______

- 8 cm2
- 16 cm2
- 24 cm2
- 32 cm2

**Q.**

Two figures are said to be __________ if they have the same size and the same shape.

**Q.**A circular park of radius 40 m is situated in a colony. Three boys Ankur, Amit and hands to talk to each other. Find the length of the string of each phone.

**Q.**If two right angled triangles are congruent, then which criteria do we use for congruency?

- S.S.S
- A.S.A
- R.H.S
- A.A.S

**Q.**

AD is one of the medians of a ∆ABC. X is any point on AD. Then, the area of ∆ABX is equal to

ar Δ CXD)

ar Δ BXC)

ar Δ ACX)

ar Δ BXD)

**Q.**In a triangle ABC, E is the mid point of median AD. Show that ar(BED)=1/4 ar(ABC)

**Q.**

If 1, 2, 3 and 4 represent the areas of the four triangles of a parallelogram with different shades, then 1=2 ≠ 3=4

True

False

**Q.**In ΔABC, E is the mid-point of median AD such that BE produced meets AC at F. IF AC = 10.5 cm, then AF =

(a) 3 cm

(b) 3.5 cm

(c) 2.5 cm

(d) 5 cm

**Q.**ABCD is a parallelogram in which BC is produced to E such that CE=BC.AE intersects CD at G. If ar(DFD)=3 cm

^{2}find the area of the parallelogram(ABCD).

**Q.**ABC is a triangle in which D is the mid-point of BC. E and F are mid-points of DC and AE respectively. IF area of ΔABC is 16 cm

^{2}, find the area of ΔDEF.

**Q.**In ∆ABC, if E is the mid-point of median AD, prove that $\mathrm{ar}(\u2206BED)=\frac{1}{4}\mathrm{ar}(\u2206ABC)$.

**Q.**If AD is median of ΔABC and P is a point on AC such that

ar (ΔADP) : ar (ΔABD) = 2 : 3, then ar (Δ PDC) : ar (Δ ABC)

(a) 1 : 5

(b) 1 : 5

(c) 1 : 6

(d) 3 : 5

**Q.**

In a triangle ABC, E is the mid-point of median AD. Show that ar (ΔBED) = 14ar(ΔABC) [2 MARKS]

**Q.**

**Question 1**

In the figure, PSDA is a parallelogram. Points Q and R are taken on PS such that PQ = RS and PA || QB || RC. Prove that ar (PQE) = ar (CFD).

**Q.**Show that the median of a triangle divides it into two triangles of equal area.

**Q.**D is the mid-point of side BC of ΔABC and E is the mid-point BD. If O is the mid point of AE, then prove that ar(ΔBOE) = $\frac{1}{8}$ ar(ΔABC).

**Q.**In triangle PQR , S is any point on PR such that PS : SE= 2 : 3 , V is a point on QS such that QV:VS = 1: 3. If ST is median of SVR and ar(STR) -ar( QVT) =12cm, then find area of PQR

**Q.**In ∆ABC, D is the midpoint of AB and P is any point on BC. If CQ || PD meets AB in Q, then prove that $\mathrm{ar}(\u2206BPQ)=\frac{1}{2}\mathrm{ar}(\u2206ABC)$.

**Q.**

In the given figure, E is any point on median AD of a ΔABC. Show that

ar (ABE) = ar (ACE)

**Q.**In the given figure, BD || CA, E is the midpoint of CA and $BD=\frac{1}{2}CA$. Prove that ar(∆ABC) = 2 × ar(∆DBC).

**Q.**Show that the diagonals of a || gm divide into four triangles of equal area.

Figure