# Solution - Pythagoras Theorem

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ConceptPythagoras Theorem

#### Question

Sides of triangle are given below. Determine it is a right triangle or not? In case of a right triangle, write the length of its hypotenuse.

50 cm, 80 cm, 100 cm

#### Solution

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Sides of triangle are given below. Determine it is a right triangle or not? In case of a right triangle, write the length of its hypotenuse.

13 cm, 12 cm, 5 cm

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In the given figure, AD is a median of a triangle ABC and AM ⊥ BC. Prove that:

1)AC^2 = AD^2 + BC . DM + ((BC)/2)^2

2) AB^2 = AD^2 – BC . DM + ((BC)/2)^2

3) AC^2 + AB^2 = 2 AD^2 + 1/2(BC)^2

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ABC is an isosceles triangle with AC = BC. If AB2 = 2AC2, prove that ABC is a right triangle.

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ABC is an equilateral triangle of side 2a. Find each of its altitudes.

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In the following figure, O is a point in the interior of a triangle ABC, OD ⊥ BC, OE ⊥ AC and OF ⊥ AB. Show that

(i) OA2 + OB2 + OC2 − OD2 − OE2 − OF2 = AF2 + BD2 + CE2

(ii) AF2 + BD2 + CE= AE2 + CD2 + BF2

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#### Reference Material

Solution for concept: Pythagoras Theorem. For the course 8th-10th CBSE
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