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In ∆ABC, seg AP is a median. If BC = 18, AB2 + AC2 = 260, Find AP.
Concept: Apollonius Theorem
∆ABC is an equilateral triangle. Point P is on base BC such that PC = `1/3`BC, if AB = 6 cm find AP.
Concept: Theorem of Similarity in Right Angled Triangle
Find the length of the hypotenuse in a right angled triangle where the sum
of the squares of the sides making right angle is 169.
(A)15 (B) 13 (C) 5 (D) 12
Concept: Theorem of Similarity in Right Angled Triangle
Prove that, in a right angled triangle, the square of the hypotenuse is
equal to the sum of the squares of remaining two sides.
Concept: Theorem of Similarity in Right Angled Triangle
If hypotenuse of a right angled triangle is 5 cm, find the radius of
the circle passing through all vertices of the triangle.
Concept: Apollonius Theorem
In right angled triangle PQR,
if ∠ Q = 90°, PR = 5,
QR = 4 then find PQ and hence find tan R.
Concept: Theorem of Similarity in Right Angled Triangle
In right-angled triangle PQR, if ∠P = 60°, ∠R = 30° and PR = 12, then find the values of PQ and QR.
Concept: Property of 30°- 60°- 90° Triangle Theorem
Choose the correct alternative:
ΔABC and ΔDEF are equilateral triangles. If ar(ΔABC): ar(ΔDEF) = 1 : 2 and AB = 4, then what is the length of DE?
Concept: Theorem of Similarity in Right Angled Triangle
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
In ΔPQR, seg PM is the median. If PM = 9, PQ2 + PR2 = 290, Find QR.
Concept: Apollonius Theorem
In ΔDEF, if ∠E = 90°, then find the value of ∠D + ∠F.
Concept: Property of 30°- 60°- 90° Triangle Theorem
Find the side and perimeter of a square whose diagonal is `13sqrt2` cm.
Concept: Application of Pythagoras Theorem
In ΔABC, seg AP is a median. If BC = 18, AB2 + AC2 = 260, then find the length of AP.
Concept: Apollonius Theorem
Out of given triplets, which is not a Pythagoras triplet?
Concept: Apollonius Theorem
From given figure, In ∆ABC, AB ⊥ BC, AB = BC then m∠A = ?
Concept: Application 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: Theorem of Similarity in Right Angled Triangle
A congruent side of an isosceles right angled triangle is 7 cm, Find its perimeter.
Concept: Theorem of Similarity in Right Angled Triangle
As shown in figure, LK = `6sqrt(2)` then (1) MK = ? (2) ML = ? (3) MN = ?
Concept: Property of 30°- 60°- 90° Triangle Theorem
