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Big Ideas Math Integrated I, 2016

BI

Big Ideas Math Integrated I, 2016 View details

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Exercise 7 Page 651

Notice that we have two right triangles where a leg and the hypotenuse from each are congruent to the corresponding part of the other.

See solution.

Practice makes perfect

From the diagram, we see that △ ADC and △ BDE are both right triangles. Additionally, since a pair of legs and the hypotenuses of the triangles are congruent, we use the HL Congruence Theorem to prove that these triangles are congruent.

Since AD and BD are congruent corresponding sides, it must be that △ ABD is an isosceles triangle where ∠ 1 and ∠ 2 are the base angles.

By the Base Angles Theorem, we know that ∠ 1 and ∠ 2 are congruent.

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Exercises p.651