AAA Similarity

Q. Which of the following divides a triangle into two triangles of equal areas?

1. Median
2. Altitude
3. Centroid
4. Hypotenuse

Q. In the given figure, $\text{AP}=\text{BP}$ and $\text{CP}=\text{DP}$. Which of the following statements is true?

1. $\Delta \mathrm{APC}\cong \Delta \mathrm{BPD}$ by $\text{ASA}$ criterion
2. $\Delta \mathrm{APC}\cong \Delta \mathrm{BPD}$ by $\text{SSS}$ criterion
3. $\text{AC}||\text{BD}$
4. None of the above

Q. Which of the following divides a triangle into two triangles of equal areas?

1. Median
2. Altitude
3. Centroid
4. Hypotenuse

Q. If AB is parallel to CD, then x = ___ degrees.

1. 36
2. 54
3. 144
4. 63

Q. If all the three altitudes of a triangle are equal, then the triangle is equilateral.

1. True
2. False

Q.

Given: $\angle GHE=\angle DFE={90}^{\circ }$ (IMAGE)

$DH=8,DF=12,DG=3x-1$ and $DE=4x+2.$ Find the
lengths of segments $DG$ and $DE$.

Q. In the adjacent figure $ABCD$ is a parallelogram $ABEF$ is a rectangle show that $△AFD\cong △BEC$

Q. What is the minimum number of pairs of equal corresponding angles required to make two triangles similar? (2 marks)

Q.

The triangles $\Delta$ ABC and $\Delta$ PQC are similar by which similarity criteria?

Q. In figure below if DE || BC then x equals :

1. 6 cm
2. 7 cm
3. 3 cm
4. 4 cm

Q.

In order to confirm whether two triangles are similar based on their angles, the values of how many angles are required?

1. 3 angles of 1 triangle and 1 angle of the other triangle

2. 2 angles of 1 triangle

3. Any 2 angles of each of the two triangles

4. All angles of 1 triangle

Q. The angles of a triangle are in the ratio $1:3:5$ then the greatest angle is

1. $\frac{5\pi }{9}$
2. $\frac{2\pi }{9}$
3. $\frac{7\pi }{9}$
4. $\frac{11\pi }{9}$

Q. In $△$ ABC, the medians $BP$ and $CQ$ are produced upto points M and N respectively such that $BP=PM$ and $CQ=QN$. Hence, A is the mid-point of MN.
If the above statement is true then mention answer as 1, else mention 0 if false.

Q. Which of the following does not represent a triangle?

1. $\Delta XYZ$
2. $\Delta DEF$
3. $\angle PQR$
4. $\Delta ABC$