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6. There are two parallel lines / and m. Three triangles ABC, PBC and QBC drawn on the same base BC on line m and the vertices A, P and Q all lie on the line l.QAP1mCBConsider the median and altitude drawn from the vertices A, P and Q for the triangles ABC, PBC andQBC respectively. Answer the following questions,(YES/NO)i) Will all the three altitudes (from vertices A, P and Q) be of same length?(YES / NO)ii) Will all the three medians (from vertices A, P and Q) be of same length? |
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Answer» et ABC be a triangle AH the HEIGHT from A to BC and AM the median (M the midpoint between B and C) without loss of generality let's say that H is between B and M so we have ΔBAH and ΔMAH CONGRUENT as angles BHA and MHA are equal angle BAH and MAH are equal (per hypothesis of problem) and they SHARE side AH. Therefore BM=HM(orHM=21BM) So, Lets' see ΔAHC. AM is bisector therefore we have ratios MCMH=ACAH but MH=21MB=21MCtherefore MCMH=21So AHC is a right angled triangle at H and AC=2AH. So, sinC=21 and C=300∠HAC=600 and ∠HAB=∠HAM=21∠HAC=300 So ∠BAC=900So, ∠BAD=60 |
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