If the bisector of the vertical angle of a triangle bisects the base also, then the triangle is isosceles. 

In the figure, in $△ABC, AB=AC=10 \text{cm} \text{and} BC=12 \text{cm}.$ $P \text{and} Q$ are the midpoints of $AB \text{and} AC$ respectively. $PM \text{and} RN$ are perpendiculars on $SQ$. If $BS : SR : RC=1 : 2 : 1$, then the length of $MN$ is:

In a quadrilateral $ACBD, AC=AD$ and $AB$ bisects $\angle A$(see figure). Show that $△ABC\cong △ABD$. What can you say about $BC$ and $BD?$     

In the figure given below, $M$ is the mid-point of $AB \text{and} \angle DAB=\angle CBA\text{ and} \angle AMC=\angle BMD$. Then the triangle $ADM$ is congruent to the triangle $BCM$ by______.

In the figure $ABC$ is an equilateral triangle with side $14$ cm. $AX=\frac{1}{3}AB, BY=\frac{1}{3}BC \text{and} CZ=\frac{1}{3}AC$. What is the area (in ${\mathrm{cm}}^2$ ) of $△PQR$?

As shown in the following figure, in $△LMN$ and $△PMN, LM=PN, LN=PM$. Write the test which assures the congruence of the two triangles. Write their remaining congruent parts

If  $\widehat{AB}\cong \widehat{CD}$, then

In figure, $\angle P\cong \angle R$, $\mathrm{seg} PQ\cong \mathrm{seg} RQ$. Prove that, $△PQT\cong △RQS$

In $\Delta ABC$, segment $AD$ and segment $BE$ are altitudes and $AE=BD$. Prove that segment $AD\cong$ segment $BE$.

In figure, if $\mathrm{\angle }\mathrm{A}\mathrm{O}\mathrm{B}=125°$, then $\mathrm{\angle }\mathrm{DOC}$ is equal to

$∆ABC$ is isosceles in which $AB=AC$. Segment $BD$ and segment $CE$ are medians. Show that $BD=CE$.

Observe the information shown in pairs of triangles given below. State the test by which the two triangles are congruent. Write the remaining congruent parts of the triangles.

From the information shown in the figure.,

 In $△PTQ=△STR$

 $\angle PTQ=\angle STR$ ..... vertically opposite angles

 seg $TQ\cong$ seg $TR$

 $△PTQ\cong △STR$....._____ test

$\angle TPQ\cong$ _____ .....corresponding angles of congruent triangles.

_____ $\cong \angle TRS$ .....corresponding angles of congruent triangles.

seg $PQ\cong$ _____ ..... corresponding sides of congruent triangles.