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

In the given triangle ABC, angle A is 90° and segment AD is perpendicular to segment BC.

The figure shows triangle ABC with right angle at A and segment AD. Point D is on side BC.

Part A: Identify a pair of similar triangles. (2 points)

Part B: Explain how you know the triangles from Part A are similar. (4 points)

Part C: If DB = 9 and DC = 4, find the length of segment DA. Show your work. (4 points)

Question

alaalcel602 alaalcel602

11-07-2022
Mathematics

contestada

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

In the given triangle ABC, angle A is 90° and segment AD is perpendicular to segment BC.

The figure shows triangle ABC with right angle at A and segment AD. Point D is on side BC.

Part A: Identify a pair of similar triangles. (2 points)

Part B: Explain how you know the triangles from Part A are similar. (4 points)

Part C: If DB = 9 and DC = 4, find the length of segment DA. Show your work. (4 points)

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olayemiolakunle65 olayemiolakunle65 · Answer 1 · 2022-07-12T22:00:35+02:00

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 [tex]90^{o}[/tex]. 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,

[tex]/Hypotenus/^{2}[/tex] = [tex]/Adjacent 1/^{2}[/tex] + [tex]/Adjacent 2/^{2}[/tex]

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,

[tex]/Hypotenus/^{2}[/tex] = [tex]/Adjacent 1/^{2}[/tex] + [tex]/Adjacent 2/^{2}[/tex]

[tex]/13/^{2}[/tex] = [tex]/Adjacent 1/^{2}[/tex] + [tex]/Adjacent 2/^{2}[/tex]

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;

[tex]5^{2}[/tex] = [tex]x^{2}[/tex] + [tex]4^{2}[/tex]

25 - 16 = [tex]x^{2}[/tex]

[tex]x^{2}[/tex] = 9

x = 3

Therefore, segment AD is 3.

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

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