Converse of Thales Theorem

Q. A girl of height $90cm$ is walking away from the base of a lamp post at a speed of $1.2m/sec$. If the lamp post is $3.6m$ above the ground, find the length of her shadow after 4 seconds.

Q. In triangle ABC, D and E are the points on sides AB and AC respectively. If AB = 18 cm, AD = 8 cm, AE = 12 cm and EC = 15 cm, then .

1. DE || BC
2. DE = BD
3. AE = AD
4. ∠ADE = ∠ACB

Q.

In below shown figure, $\frac{PS}{SQ}=\frac{PT}{TR}$ and$\angle PST=\angle PRQ$. Then $\Delta PQR$ is a/an __ ____triangle.

1. Equilateral
2. Isosceles
3. Scalene
4. Right angled

Q.

$\text{In the following figure, triangle AXY}\text{is isosceles with}\angle AXY=\angle AYX.$

$\text{If}\frac{BX}{AX}=\frac{CY}{AY},\text{then prove that}\text{triangle ABC is an isosceles triangle.}$

Q. In $\Delta$ ABC, $\frac{AD}{DB}=\frac{AE}{EC}$ and $\angle$ ADE = $\angle$ ACB. Then $\Delta$ ABC is a/an

1. equilateral

2. isosceles

3. right angled

4. scalene

Q.
In $\Delta ABC$, $\frac{AD}{DB}=\frac{AE}{EC}$ and $\angle ADE$ = $\angle ACB$. Then $\Delta ABC$ is

1. an isosceles triangle.
2. a right angled triangle.
3. an equilateral triangle.
4. a scalene triangle.

Q. In $\Delta ABC$, D and E lie on the line AB and AC respectively, as shown in the figure.
$\angle AED$ is:

1. 40

Q. In the figure shown below , if $\frac{PS}{SQ}$= $\frac{PT}{TR}$ and$\angle$PST= $\angle$PRQ, then $\Delta$PQR is a/an triangle.

1. isosceles
2. equilateral
3. right angled
4. scalene

Q. In triangle ABC, D and E are the points on sides AB and AC respectively. If AB = 18 cm, AD = 8 cm, AE = 12 cm and EC = 15 cm, then .

1. DE = BD
2. ∠ADE = ∠ACB
3. AE = AD
4. DE || BC

Q. In triangle ABC, D and E are the points on sides AB and AC respectively. If AB = 18 cm, AD = 8 cm, AE = 12 cm and EC = 15 cm, then .

1. DE = BD
2. ∠ADE = ∠ACB
3. AE = AD
4. DE || BC

Q. In triangle ABC, D and E are two points on AB an AC respectively. If AD : DB = AE : EC, then which is correct?

1. DE is perpendicular to BC
2. DE is parallel to BC
3. DE is parallel to AB
4. DE is parallel to AC

Q.

In $\Delta ABC$, point D and E lies on the line AB and AC respectively as shown in the figure. Find the measure of $\angle AED$.

1. ${65}^{\circ }$

2. ${40}^{\circ }$

3. ${75}^{\circ }$

4. ${70}^{\circ }$