Hypotenuse Leg Congruence

Q.

$\mathrm{CDE}$is an equilateral triangle formed on a side $\mathrm{CD}$ of a square $\mathrm{ABCD}$(Figure).

Show that $\mathrm{\Delta }\mathrm{ADE}\cong \mathrm{\Delta }\mathrm{BCE}$.

Q.
The diagonal $AC$ divides the rectangle $ABCD$ into two triangles. Are the two triangles congruent? If so, what are all the laws of congruency that can be used to prove it?

1. No
2. Yes, All congruency laws
3. Yes, only S.A.S and S.S.S

Q. Are the triangles in the following diagrams congruent?

1. No
2. Yes

Q. Find the congruency criteria for $\Delta AOB$ and $\Delta COD$.

Q. Select the appropriate option for the given figure, if $AD\text{and}BC$ are both perpendicular to $AB$, and $BD\text{and}AC$ are equal in length.

1. $△ABC\cong △ABD$
2. $△ABC\cong △BAD$
3. $△ABC\cong △BDA$
4. $\text{Triangles not congruent}$

Q. Which of the following pair of triangles are congruent by the hypoteneous leg congruency condition?

1. 
2. 
3. 
4. All of the above

Q. In the isosceles right angled triangle $△ABC$ right angled at $B$, the perpendicular is drawn to the hypotaneus which meet hypotaneus at $D$.
Choose the correct option.

1. $△ABD\cong △CBD$
2. $D$ bisects side $AC$
3. Both $\left(a\right)$ and $\left(b\right)$ correct
4. None correct

Q. Which two triangles are congruent and by which congruent condition. ?

1. $\Delta$ $\text{ABC}\cong$ $\Delta$ $\text{DEC}\left(\text{Hypotenuse Leg}\right)$
2. $\Delta$ $\text{ABC}\cong$ $\Delta$ $\text{CED}\left(\text{SAS}\right)$
3. $\Delta$ $\text{CAB}\cong$ $\Delta$ $\text{DEC}\left(\text{ASA}\right)$
4. All are correct

Q. There is a triangle $△ABC$ two perpendiculars which are equal in length are drawn to sides $AB$ and $AC$ from the vertices $C$ and $B$ respectively. Now, consider the statements below.

1. $△ABC$ is an isosceles triangle.
2. $△BCD\cong △CBE$
3. $△ABE\cong △ACD$

Which of the above statement is correct?

1. $1$ and $2$ only
2. $2$ and $3$ only
3. $1$ and $3$ only
4. $1$, $2$ and $3$

Q. Which of the following congruency rule satisfies congruency of both given triangles using given information only.

1. Side-Side-Side
2. Side-Angle-Side
3. Angle-Side-Angle
4. Hypotenuse Leg Congruency