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photoshop1234 [79]
3 years ago
10

In the given figure ABCD is a parallelogram, E is the midpoint of BC. DE produced meets AB produced at L. Prove that AB = B L an

d AL=2DC​

Mathematics
1 answer:
aliina [53]3 years ago
7 0

Answer:

<em>See Reasoning Below</em>

Step-by-step explanation:

To prove that AB = BL, or in other words AB ≅ BL, let us consider the triangles CED and BEL. If we were to prove they were congruent, then by CPCTC ( corresponding parts of congruent triangle are congruent ) DC ≅ BL. As AB ≅  DC by " Properties of Parallelogram " it would be that through transitivity, AB ≅ BL / AB = BL;

m

Now for " part 2 " we can consider that AB = DC, from part 1. If AB = BL, then AL = 2 ( AB ) by the Partition Postulate. AB = DC, so we can also say that AL = 2 ( DC ) - Proved

See attachment in statement reasoning form for part 1;

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