Question
In triangles ABC and CDE, if AC = CE, BC = CD, $\angle\text{A}=60^\circ,\angle\text{C}=30^\circ$ and $\angle\text{D}=90^\circ.$ Are two triangles congruent?
✓
Answer
For the triangles ABC and ECD, we have the following information and corresponding figure:$\text{AC}=\text{CE}$
$\text{BC}=\text{CD}$
$\angle\text{}A=60^\circ$
$\angle\text{C}=30^\circ$
$\angle\text{D}=90^\circ$
In triangles ABC and ECD, we have$\text{AC}=\text{EC}$
$\text{BC}=\text{CD}$
and $\angle\text{BAC}=\angle\text{CED}$ The SSA criteria for two triangles to be congruent are being followed. So both the triangles are congruent.
$\text{BC}=\text{CD}$
$\angle\text{}A=60^\circ$
$\angle\text{C}=30^\circ$
$\angle\text{D}=90^\circ$
In triangles ABC and ECD, we have$\text{AC}=\text{EC}$$\text{BC}=\text{CD}$
and $\angle\text{BAC}=\angle\text{CED}$ The SSA criteria for two triangles to be congruent are being followed. So both the triangles are congruent.
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
In the adjoining figure, ABCD is a parallelogram in which $\angle\text{A}=70^{\circ}.$ Calculate $\angle\text{B},\angle\text{C}$ and $\angle\text{D}.$
→Draw the graph of the following linear equations in two variables:
x + y = 4
x + y = 4
Prove that the perimeter of a triangle is greater than the sum of its altitudes.
Using factor theorem, factorize the following polynomials:
$y^3 - 7y + 6$
→$y^3 - 7y + 6$
If $(x-1)^3=8$, What is the value of $(x+1)^2$ ?
→The measure of one of the angles of a triangle is twice the measure of its smallest angle and the measure of the other is thrice the measure of the smallest angle. Find the measures of the three angles.
In Q.No. 7, what is the probability of getting at least two heads?
In fig. PQRS is a square and SRT is an equilateral triangle. Prove that:
→- PT = QT.
- $\angle\text{TQR}=15^\circ.$
The sum of two angles of a triangle is equal to its third angle. Determine the measure of the third angle.
Plot the following points on the graph paper:
(2, 5)
(2, 5)