Question

Seth is using the figure shown below to prove Pythagorean Theorem using triangle similarity.

Answer 1

The Pythagorean theorem is one that can be used to determine the third unknown side of a given right-angled triangle. Thus the answers required are:

• A pair of similar triangles formed are ΔABD and ΔADC
• Segment AD is a perpendicular bisector of segment BC, and also bisects angle A in two equal measures
• Segment AD = 3

A right-angled triangle is one which has the measure of one of its internal angles equal to $90^{o}$. Thus to determine the value of one of its unknown sides, the Pythagoras theorem can be used.

Pythagora theorem states that: for a right-angled triangle,

$/Hypotenus/^{2}$ = $/Adjacent 1/^{2}$ + $/Adjacent 2/^{2}$

Thus from the given question, we have;

Part A: A pair of similar triangles formed are ΔABD and ΔADC.

Part B: In the given triangle, segment AD is a perpendicular bisector of segment BC. Thus segment AD also bisects angle A in two equal measures. So triangle ABC is now divided into two equal pairs i.e ΔABD and ΔADC.

Part C: Given that: If DB = 9 and DC = 4, find the length of segment DA.

Let segment AD be represented by x, so that;

from ΔABC,

$/Hypotenus/^{2}$ = $/Adjacent 1/^{2}$ + $/Adjacent 2/^{2}$

$/13/^{2}$ = $/Adjacent 1/^{2}$ + $/Adjacent 2/^{2}$

Thus the appropriate Pythagorean triple for this question is 5, 12, 13.

So that AB = 12, AC = 5 and BC = 13

Let segment AD be represented by x.

Thus from triangle ADC, applying the Pythagoras theorem we have;

$5^{2}$ = $x^{2}$ + $4^{2}$

25 - 16 = $x^{2}$

$x^{2}$ =   9

x = 3

Therefore, segment AD is 3.

For more clarifications on Pythagoras theorem, visit: brainly.com/question/343682

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