Triangles

Q.

All the following are criteria for measuring the congruency of triangles except the _____.

1. SSS

2. ASA

3. SAS

4. AAA

Q. In a $\Delta ABC,AB=10cm,BC=12cm,andAC=14cm.$ Find the length of median AD. If G is the centroid, find length of GA :

1. $4\sqrt{7},\frac{8}{3}\sqrt{7}$
2. $\frac{10}{\sqrt{3}},\frac{8}{3}\sqrt{7}$
3. $\frac{5}{3}\sqrt{7},\frac{5}{9}\sqrt{7}$
4. $5\sqrt{7},4\sqrt{7}$

Q. In the triangle ABC, BC = CD and $(\angle ABC-\angle BAC)={30}^{\circ }$. The measure of $\angle ABD$ is :

1. ${30}^{\circ }$
2. ${45}^{\circ }$
3. ${15}^{\circ }$
4. $Ca{n}^{\prime }tbedetermined$

Q. Find the length of AC in right angled triangle ABC which has a circle inscribed in it, that touches the sides AB, BC and CA at D, E and F respectively, and has AD = 6 cm and BE = 5 cm.

1. 41 cm
2. 55 cm
3. 44 cm
4. 61 cm

Q. ABC is a triangle in which $\angle CAB={80}^{\circ }and\angle ABC={50}^{\circ }$. AE, BF and CD are the altitudes and O (intersection point of AE, BF, and CD) is the orthocentre. What is the value of $\angle AOB$?

1. ${130}^{\circ }$
2. ${65}^{\circ }$
3. ${70}^{\circ }$
4. ${50}^{\circ }$

Q. From a point O in the interior of a $\Delta ABC$. Perpendiculars OD, OE and OF are drawn to the sides BC, CA and AB respectively, then which one of the following is true?

1. $A{F}^2+B{D}^2+C{E}^2=O{D}^2+O{E}^2+O{F}^2$
2. $A{F}^2+B{D}^2+C{E}^2=A{E}^2+C{D}^2+B{F}^2$
3. $A{B}^2+B{C}^2=A{C}^2$
4. $A{F}^2+B{D}^2+C{E}^2=O{A}^2+O{B}^2+O{C}^2$

Q. In the adjoining figure, if AB, SC and TD are perpendicular to BD with the length indicated, then $\frac{x}{y}$ is equal to:

1. $\frac{p}{p+q}$
2. $\frac{q}{p}$
3. $\frac{p}{q}$
4. $\frac{q}{p+q}$

Q. In the figure, AD = 12 cm, AB = 20 cm and AE = 10 cm. Find EC:

1. 14 cm
2. 8 cm
3. 15 cm
4. 10 cm

Q. In the given figure, AD is the external bisector of $\angle EAC,$ intersects BC produced to D. If AB = 12 cm, AC = 8 cm and BC = 4 cm, find CD.

1. 10 cm
2. 6 cm
3. 8 cm
4. 9 cm

Q. In the triangle ABC, MN is parallel to AB. Area of trapezium ABNM is twice the area of triangle CMN. What is ratio of CM : AM ?

1. $\frac{\sqrt{3}-1}{2}$
2. $\frac{\sqrt{3}+1}{2}$
3. $Noneofthese$
4. $\frac{1}{\sqrt{3}+1}$