In the figure- it is given that AE - AD and BD - CE- Prove that triangle AEB is congruent triangle ADC-

Question

Toppr Admin · Accepted Answer

We have AE-AD and CE-BD-xA0-Adding- we get AE-CE-AD-BD-x21D2-AC-AB-In triangles AEB and ADC- we haveAE-AD - -given-AB-AC - -proved-x2220-EAB-x2220-DAC- -xA0- -common angle-By SAS postulate -x25B3-AEB-x2245-x25B3-ADC-

In the figure, it is given that AE = AD and BD = CE. Prove that $△ A E B$ is congruent $△ A D C$ .

We have $A E = A D$ and $C E = B D$ .
Adding, we get $A E + C E = A D + B D$
$\Rightarrow A C = A B$ .
In triangles $A E B$ and $A D C$ , we have
$A E = A D$ ....... (given);
$A B = A C$ ....... (proved);
$∠ E A B = ∠ D A C$ , (common angle).
By SAS postulate $△ A E B ≅ △ A D C$ .

In the figure, it is given that AE = AD and BD = CE. Prove that △AEB is congruent △ADC.

We have AE=AD and CE=BD. Adding, we get AE+CE=AD+BD⇒AC=AB.In triangles AEB and ADC, we haveAE=AD ....... (given);AB=AC ....... (proved);∠EAB=∠DAC, (common angle).By SAS postulate △AEB≅△ADC.

In the figure, it is given that AE = AD and BD = CE. Prove that $△ A E B$ is congruent $△ A D C$ .

We have $A E = A D$ and $C E = B D$ .
Adding, we get $A E + C E = A D + B D$
$\Rightarrow A C = A B$ .
In triangles $A E B$ and $A D C$ , we have
$A E = A D$ ....... (given);
$A B = A C$ ....... (proved);
$∠ E A B = ∠ D A C$ , (common angle).
By SAS postulate $△ A E B ≅ △ A D C$ .