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Standard IX

Mathematics

Proof for Validation for Construction of a Triangle with Given Perimeter and Two Base Angles

In the given ...

Question

In the given pairs of triangles, applying only the ASA congruence criterion, determine which triangles are congruent. Also, write the congruent triangles in symbolic form.

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Solution

In $△ A B D$ and $△ C D B$
$B D = B D$ [Common]
$∠ A B D = ∠ C D B = 30^{o}$ [Given]
$∠ A D B = ∠ C B D = 40^{o}$ [Given]

$∴ △ A B D ≅ △ C D B$ [ASA criterion]

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In the given pairs of triangles, applying only the ASA congruence criterion, determine which triangles are congruent. Also, write the congruent triangles in symbolic form.

In △ABD and △CDBBD=BD [Common]∠ABD=∠CDB=30o [Given]∠ADB=∠CBD=40o [Given]∴△ABD≅△CDB [ASA criterion]

In $△ A B D$ and $△ C D B$
$B D = B D$ [Common]
$∠ A B D = ∠ C D B = 30^{o}$ [Given]
$∠ A D B = ∠ C B D = 40^{o}$ [Given]

$∴ △ A B D ≅ △ C D B$ [ASA criterion]