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LEGF congruent to LBGC prove BE is bisected by ZAGC that Given - 3 B...

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LEGF congruent to LBGC prove BE is bisected by ZAGC that Given - 3 B

LEGF congruent to LBGC prove BE is bisected by ZAGC that Given - 3 B



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$$\begin{array}{c} \text { Given: } \mathrm{AB}=\mathrm{DE}, \mathrm{BC}=\mathrm{EF} \\ \text { and } \mathrm{AC}=\mathrm{DF} \\ \text { Prove: } \quad \triangle \mathrm{ABC} \cong \triangle \mathrm{DEF} \end{array}$$ To prove the triangles congruent, we will draw a third triangle and show that $\triangle \mathrm{ABC}$ and $\triangle \mathrm{DEF}$ are both congruent to it. $$\triangle \mathrm{APC} \cong \triangle \mathrm{DEF}$$ S.A.S. postulate. (GRAPH CANT COPY)

Well, there been off Triangle ABC and the

We have problem # 15. Uh in this there is an equilateral triangle abc. Okay, let's draw the creative tangle first, then we'll move further. A. B. C. Is an equilateral triangle. And he is the point inside businesses that be equal to one x 3 busy Be equal to one x 3 B. C. So they should be here, they should be here. Okay, we have to prove that 980 square equal to seven AB square since the Squire is involved. So it is certainly a case of right angle triangle. So construction drop a perpendicular E From side von Vortex A two side busy. Since the sequential tangle so be evil be equal to easy. Okay, do we know since this is an equilateral triangle? So B. E. Will be equal to E. C. Will be equal to half of Bc or half of a B. Now the E will be equal to B E minus BD. That is A B by two minus Bc by oh yeah, Bc by Bt this ability and if this is X this has to be three X. Okay, busy by two. Well okay so this is 34 X. So this has to be mhm Not busy by two. It should be busy by three because B. D. Is being given as B C. Battery. Okay, now busy becomes equal to a B as it is in a creative triangle. So a B Y tu minus A B x three which means a B by six. Yeah we'll be using this afterwards. D equal to 80 by six so D equal to a B by six. Now in right angle triangle, A B in triangle, A B right angle triangle. We'll be using the pythagoras still um from that a square will be equal to a b square minus be a square, be a square, that is a b squared minus a B by two whole square. So a b squared minus the square before. So three x 4. A b square. We'll be using this afterwards. Okay. Again, in right angle triangle A D. E. So triangle A D E. We should be writing is quite equal to 80 square minus the square. It is mm hmm 80 square minus minus a B squared by six square. That is 36. Because we had the equal to 80 x six. Okay. No, from using equation for and We have a equal to three x 4. Yeah. A country. Yes. So we should be writing three by for a b Square equal to 80 sq a b squared by 36. So three x 4, a b Squire plus a B squared by 36 equal to 80. This is 36. So nine Less of one or sorry, 27 Plus one, 28 A b square will be equal to A. D. So for seven times for nine times, so seven a b square will be equal to nine. It is quiet and stroke.

So you, uh

So we have point AP Year point point B that I think just won't be here, and this will be equitable. The


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