Tests for Congruency of Triangles

Q.

If two figures have same area, they must be ___.

1. Congruent

2. Having equal sides

3. Similar

4. 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) = $\frac{1}{4}$ar(ΔABC)

1. $\frac{1}{4}$ar(ΔABD)

2. $\frac{1}{4}$ar(ΔABC)

3. $\frac{1}{4}$ar(ΔBCD)

4. $\frac{1}{4}$ar(ΔACB)

Q.

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

1. 

2. 

3. 

4. 

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) =

1. 16 cm

2. 18 cm

3. 8 cm

4. 12 cm

Q.

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

1. Parallelogram

2. Trapezium

3. Rectangle

4. 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 cm², then Area of trapezium BFEC is______

1. 8 $c{m}^2$
2. 16 $c{m}^2$
3. 24 $c{m}^2$
4. 32 $c{m}^2$

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?

1. S.S.S
2. A.S.A
3. R.H.S
4. 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

1. ar Δ CXD)

2. ar Δ BXC)

3. ar Δ ACX)

4. 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 $1=2$ ≠ $3=4$

1. True

2. 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 cm² 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 cm², find the area of ΔDEF.

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

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) = $\frac{1}{4}$ar(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 $\mathrm{ar}(∆BPQ)=\frac{1}{2}\mathrm{ar}(∆ABC)$.

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