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Choose the correct alternative:
Out of the following which is a Pythagorean triplet?
Concept: Apollonius Theorem
In right-angled ΔABC, BD ⊥ AC. If AD= 4, DC= 9, then find BD.
Concept: Theorem of Geometric Mean
Sides of the triangle are 7 cm, 24 cm, and 25 cm. Determine whether the triangle is a right-angled triangle or not.
Concept: Converse of Pythagoras Theorem
In ΔPQR, seg PM is the median. If PM = 9, PQ2 + PR2 = 290, Find QR.
Concept: Apollonius Theorem
If the angles of a triangle are 30°, 60°, and 90°, then shown that the side opposite to 30° is half of the hypotenuse, and the side opposite to 60° is `sqrt(3)/2` times of the hypotenuse.
Concept: Right-angled Triangles and Pythagoras Property
In ΔDEF, if ∠E = 90°, then find the value of ∠D + ∠F.
Concept: Property of 30°- 60°- 90° Triangle Theorem
Choose the correct alternative:
In right-angled triangle PQR, if hypotenuse PR = 12 and PQ = 6, then what is the measure of ∠P?
Concept: Right-angled Triangles and Pythagoras Property
Find the side and perimeter of a square whose diagonal is `13sqrt2` cm.
Concept: Application of Pythagoras Theorem in Acute Angle and Obtuse Angle
In ΔABC, seg AP is a median. If BC = 18, AB2 + AC2 = 260, then find the length of AP.
Concept: Apollonius Theorem
Find the length of diagonal of the square whose side is 8 cm.
Concept: Right-angled Triangles and Pythagoras Property
Find the side of the square whose diagonal is `16sqrt(2)` cm.
Concept: Right-angled Triangles and Pythagoras Property
Choose the correct alternative:
Out of given triplets, which is not a Pythagoras triplet?
Concept: Apollonius Theorem
Choose the correct alternative:
If length of sides of a triangle are a, b, c and a2 + b2 = c2, then which type of triangle it is?
Concept: Right-angled Triangles and Pythagoras Property
From given figure, In ∆ABC, AB ⊥ BC, AB = BC then m∠A = ?
Concept: Application of Pythagoras Theorem in Acute Angle and Obtuse Angle
If a triangle having sides 50 cm, 14 cm and 48 cm, then state whether given triangle is right angled triangle or not
Concept: Converse of Pythagoras Theorem
A rectangle having dimensions 35 m × 12 m, then what is the length of its diagonal?
Concept: Converse of Pythagoras Theorem
From the given figure, in ∆ABC, if AD ⊥ BC, ∠C = 45°, AC = `8sqrt(2)` , BD = 5, then for finding value of AD and BC, complete the following activity.
Activity: In ∆ADC, if ∠ADC = 90°, ∠C = 45° ......[Given]
∴ ∠DAC = `square` .....[Remaining angle of ∆ADC]
By theorem of 45° – 45° – 90° triangle,
∴ `square = 1/sqrt(2)` AC and `square = 1/sqrt(2)` AC
∴ AD =`1/sqrt(2) xx square` and DC = `1/sqrt(2) xx 8sqrt(2)`
∴ AD = 8 and DC = 8
∴ BC = BD +DC
= 5 + 8
= 13
Concept: Property of 30°- 60°- 90° Triangle Theorem
Complete the following activity to find the length of hypotenuse of right angled triangle, if sides of right angle are 9 cm and 12 cm.
Activity: In ∆PQR, m∠PQR = 90°
By Pythagoras Theorem,
PQ2 + `square` = PR2 ......(I)
∴ PR2 = 92 + 122
∴ PR2 = `square` + 144
∴ PR2 = `square`
∴ PR = 15
∴ Length of hypotenuse of triangle PQR is `square` cm.
Concept: Similarity in Right Angled Triangles
In ∆LMN, l = 5, m = 13, n = 12 then complete the activity to show that whether the given triangle is right angled triangle or not.
*(l, m, n are opposite sides of ∠L, ∠M, ∠N respectively)
Activity: In ∆LMN, l = 5, m = 13, n = `square`
∴ l2 = `square`, m2 = 169, n2 = 144.
∴ l2 + n2 = 25 + 144 = `square`
∴ `square` + l2 = m2
∴By Converse of Pythagoras theorem, ∆LMN is right angled triangle.
Concept: Converse of Pythagoras Theorem
A congruent side of an isosceles right angled triangle is 7 cm, Find its perimeter
Concept: Similarity in Right Angled Triangles
