WebMar 22, 2024 · Example 3 In figure, AB is a diameter of the circle, CD is a chord equal to the radius of the circle. AC and BD when extended intersect at a point E. Prove that ∠ AEB = 60°. Given: AB is diameter of circle Chord CD, where CD = Radius of circle To prove: ∠AEB = 60° Construction: Join OC WebMay 26, 2024 · Solution: It is given, AC = BD. From the given figure, we get, AC = AB + BC. BD = BC + CD. ⇒ AB + BC = BC + CD [Given: AC=BD] We know that, according to Euclid’s …
jemh106kekee PDF Triangle Shape - Scribd
WebNov 7, 2024 · In Fig., if AC = BD, then prove that AB = CD.a euclid's geometry cbse 1 Answer 0 votes answered Nov 7, 2024 by sforrest072 (129k points) selected Nov 8, 2024 by jisu zahaan Best answer Given : AC = BD To prove AB = CD. AC = AB + BC BD = BC + CD As AC = BD (given) AB + BC = BC + CD ∴ AB = CD. Proved. ← Prev Question Next Question → WebIn given figure, If BD⊥AC and CE⊥AB, then prove that (i) AEC∼ ADB (ii) ABCA= DBCE Medium Solution Verified by Toppr (i) In sAEC and ADB, we have ∠AEC=∠ADB=90 0 [∵CE⊥AB and BD⊥AC] and, ∠EAC=∠DAB [Each equal to ∠A] Therefore, by AA-criterion of similarity, we have AEC∼ ADB [Hence proved] (ii) we have, AEC∼ ADB [AS proved above] … the seasons 1897
geometry - How to prove AC = BD? - Mathematics Stack Exchange
WebThe perpendicular from A on side BC of a ∆ABC intersects BC at D such that DB = 3CD (see Fig. 6.55). Prove that 2AB 2 = 2AC 2 + BC 2 Solution: In a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. In ∆ABC , AD ⊥ BC and BD = 3CD BD + CD = BC 3CD + CD = BC 4CD = BC CD = (1/4) BC ...... (1) WebIf AC = 5.7 cm, BD = 3.8 cm and CD = 5.4 cm, Find BC. Solution: Given: BD ⊥ AC AC = 5.7 cm, BD = 3.8 cm and CD = 5.4 cm ∠ABC = 90 o Required to find: BC We know that, ΔABC ∼ ΔBDC [By AA similarity] ∠BCA = ∠DCA = 90 o ∠AXY = ∠ABC [Common] Thus, AB/ BD = BC/ CD [Corresponding Parts of Similar Triangles are propositional] 5.7/ 3.8 = BC/ 5.4 WebIn Fig., ABD is a triangle right angled at A and AC ⊥ BD. Show that: (i) AB 2=BC.BD (ii) AC 2=BC.DC (iii) AD 2=BD.CD Medium Solution Verified by Toppr (i) In BCA and BAD, ∠BCA=∠BAD ....Each 90 o ∠B is common between the two triangles. So, BCA∼ BAD ...AA test of similarity .... (I) Hence, ABBC= ADAC= BDAB ...C.S.S.T my pillow national sleep foundation