Mathematics
Assertion (A): In △ABC, D is a point on side BC. AB + BC + AC > 2AD
Reason (R): Sum of two sides of a triangle is greater than the third side.
A is true, R is false
A is false, R is true
Both A and R are true
Both A and R are false
Triangles
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Answer
We know that,
Sum of two sides of a triangle is greater than the third side is fundamental property of triangle.
∴ Reason (R) is true.
In △ABD,
⇒ AB + BD > AD …(1) [Sum of any two sides of triangle is greater than the third side]
In △ADC,
⇒ AC + CD > AD …(2) [Sum of any two sides of triangle is greater than the third side]
Adding eq.(1) and (2), we have:
⇒ AB + BD + AC + CD > AD + AD
⇒ AB + AC + BD + CD > 2AD
⇒ AB + AC + BC > 2AD
∴ Assertion (A) is true.
Hence, option 3 is the correct option.
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In the given figure, the bisectors of ∠B and ∠C intersect each other at O and ∠BAC = 50°. The measure of ∠BOC is :
100°
115°
130°
140°
In the given figure, △ABD ≅ △ACD. If ∠DAC = 30° and ∠BDC = 110°, then the measure of ∠DBA is :
30°
50°
70°
25°