Using the information given in the figure- find the values of x and y-A- x-15- y-9B- x-9- y-15C- x-14- y-9D- x-15- y-10

The correct option is A x = 15, nbsp;y = 9 nbsp; Given, AB = AC 94=6x+4 6x=90 x=15 nbsp; In ABD and ACD, (i) ∠ ADB = ∠ ADC = 90^∘ ... (given) (ii) ...

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Standard IX

Mathematics

RHS Criteria for Congruency

Using the inf...

Question

Using the information given in the figure, find the values of x and y.

x = 15, y = 9

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x = 9, y = 15

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x = 14, y = 9

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x = 15, y = 10

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Solution

The correct option is A
x = 15, y = 9

Given, $A B = A C$
$⟹ 94 = 6 x + 4 ⟹ 6 x = 90 ⟹ x = 15$

In $△ A B D$ and $△ A C D$ ,
(i) $∠ A D B = ∠ A D C = 90^{\circ}$ ... (given)
(ii) AB = AC ... (given)
(iii) AD = AD ... (common side)
$\Rightarrow$ $△ A B D ≅ △ A D C$ ... (RHS congruence rule)
Then, $B D = C D$ ... (CPCT)
$\Rightarrow 2 y - 7 = 11 \Rightarrow 2 y = 18 \Rightarrow y = 9$

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Using the information given in the figure, find the values of x and y.

The correct option is A x = 15, y = 9 Given, AB=AC ⟹94=6x+4⟹6x=90⟹x=15 In △ABD and △ACD, (i) ∠ADB=∠ADC=90∘ ... (given) (ii) AB = AC ... (given) (iii) AD = AD ... (common side) ⇒△ABD≅△ADC ... (RHS congruence rule) Then, BD=CD ... (CPCT) ⇒2y–7=11⇒2y=18⇒y=9