Question

Math, not my question but @iSuckAtMath101 can't post.

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.

Answer 1

Someone has previously answered the question:

Link: https://questioncove.com/updates/5e2f2d5c4a260acf89dd9400

This should help explain it more

Answer 2

Part C; From the dimensions given in the question, triangle ABD has side BD measuring 9 while the other two sides are not given. But angle D is given as 90° (perpendicular line from angle A in the original triangle). Also, angle A has been split in two which makes angle A in triangle ABD to measure 45°

Therefore triangle ABD is a right angled triangle with the other two sides measuring 45° each. [180° = (90°+45°+45°)]

We can solve for the unknown side by applying trigonometrical ratios. We have line DB given as 9 units and the angle facing it (angle A) is 45°. Line AD is unknown and is also facing angle B which is 45°

We shall apply the ratio of tangent of angle since we have the opposite to angle B (unknown) and the adjacent to angle B (9 units)

Tan 45° = opposite/adjacent

Tan 45° = DA/9

Multiply both sides by 9

9 × Tan 45° = DA

(Looking up the table of values for trigonometrical ratios, Tan 45°=1)

9 × 1 = DA

Therefore line DA equals 9 units

So let me explain this as best as i can.

Answer 3

"But angle D is given as 90° (perpendicular line from angle A in the original triangle). Also, angle A has been split in two which makes angle A in triangle ABD to measure 45°"

So lets start with this:

Angle D is 90 degrees. Angle A was split into TWO which makes the triangle ABD 45 degrees.
So ABD "Therefore triangle ABD is a right angled triangle with the other two sides measuring 45° each. [180° = (90°+45°+45°)]" thats the problem aka solution to the ABD
Which is how we got "Tan 45° = opposite/adjacent"

The adjacent to angle B (9 units)
So,
Tan 45° = opposite/adjacent

Tan 45° = DA/9

Multiply both sides by 9

9 × Tan 45° = DA

(Looking up the table of values for trigonometrical ratios, Tan 45°=1)

9 × 1 = DA

Therefore line DA equals 9 units