Last seen: Jun 14, 2021
Given, in ΔABC, O is a point in the interior of a triangle. And OD ⊥ BC, OE ⊥ AC and OF ⊥ AB. Join OA, OB and OC 2s.png (i) By Pythagoras t...
Given, ABCD is a rhombus whose diagonals AC and BD intersect at O. 2s.png Prove that, AB2 + BC2 + CD2 + AD2 = AC2 + BD2 Since, the diagonal...
Given, ABC is an equilateral triangle of side 2a. 2s.png Draw, AD ⊥ BC In ΔADB and ΔADC, AB = AC AD = AD ∠ADB = ∠ADC [Both are 90°] T...
Given, ΔABC is an isosceles triangle having AC = BC and AB2 = 2AC2 2s.png In ΔACB, AC = BC AB2 = 2AC2 AB2 = AC2 + AC2 = AC2 + BC2 [Sinc...
Given, ΔABC is an isosceles triangle right angled at C. 2s.png In ΔACB, ∠C = 90° AC = BC (By isosceles triangle property) AB2 = AC2 + BC2 [...
(i) In ΔADB and ΔCAB, ∠DAB = ∠ACB (Each 90°) ∠ABD = ∠CBA (Common angles) ∴ ΔADB ~ ΔCAB [AA similarity criterion] ⇒ AB/CB = BD/AB ⇒ AB2 = CB ...
Given, ΔPQR is right angled at P is a point on QR such that PM ⊥QR 2s.png We have to prove, PM2 = QM × MR In ΔPQM, by Pythagoras theorem PQ...
(i) Given, sides of the triangle are 7 cm, 24 cm, and 25 cm. Squaring the lengths of the sides of the, we will get 49, 576, and 625. 49 + 576 = 62...
Sides of two similar triangles are in the ratio 4 : 9. 2s.png Let ABC and DEF are two similar triangles, such that, ΔABC ~ ΔDEF AB/DE = AC/...
Given, ΔABC and ΔBDE are two equilateral triangle. D is the midpoint of BC. 2s.png ∴ BD = DC = 1/2BC Let each side of triangle is 2a. As, Δ...
2s.png Given, ABCD is a square whose one diagonal is AC. ΔAPC and ΔBQC are two equilateral triangles described on the diagonals AC and side BC of ...
AM and DN are the medians of triangles ABC and DEF respectively and ΔABC ~ ΔDEF. 2s.png Area(ΔABC)/Area(ΔDEF) = AM2/DN2 Since, ΔABC ~ ΔDEF (G...
Given, D, E and F are respectively the mid-points of sides AB, BC and CA of ΔABC. 2s.png In ΔABC, F is the mid-point of AB (Already given) ...
Given, ΔABC and ΔPQR are two similar triangles and equal in area 2s.png Now let us prove ΔABC ≅ ΔPQR. Since, ΔABC ~ ΔPQR ∴ Area of (ΔABC)/A...
We know that ABC and DBC are two triangles on the same base BC. AD intersects BC at O. Area (ΔABC)/Area (ΔDBC) = AO/DO Let us draw two perpen...
Given, ABCD is a trapezium with AB || DC. Diagonals AC and BD intersect each other at point O. 2s.png In ΔAOB and ΔCOD, we have ∠1 = ∠2 (Alte...
Given, ΔABC ~ ΔDEF, Area of ΔABC = 64 cm2 Area of ΔDEF = 121 cm2 EF = 15.4 cm As we know, if two triangles are similar, ratio of their area...
Given, ΔABC ~ ΔPQR 2s.png We know that the corresponding sides of similar triangles are in proportion. ∴ AB/PQ = AC/PR = BC/QR ……………(i) Als...
Given, Length of the vertical pole = 6m Shadow of the pole = 4 m Let Height of tower = h m Length of shadow of the tower = 28 m In ΔABC and ΔD...
Two triangles ΔABC and ΔPQR in which AD and PM are medians such that; AB/PQ = AC/PR = AD/PM We have to prove, ΔABC ~ ΔPQR Let us construct first...