Question

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

Answer 1

Part A: A pair of similar triangles is triangle DEF and triangle GFD.

Part B: Traingle DEF ~ triangle GFD by the AA Similarity Theorem

Part C: By applying the Leg Rule, the length of segment ED = 4 units.

Recall:

• Based on the Angle-Angle Similarity Theorem (AA) two triangles that have two pairs of congruent triangles can be proven to be similar to each other.
• In a right triangle where the altitude intersects the hypotenuse, the Leg Rule applies, which is: Hypotenuse/Leg = Leg/Part

The Figure of the given triangle DEF is shown in the attachment below.

Part A: A Pair of Similar Triangles

A pair of similar triangles are traingle DEF and triangle GDF

Part B: Reason for Similarity

Triangle DEF and GDF have two pairs of congruent angles, ∠EDF ≅∠DGF and ∠EFD ≅∠GFD.

• Therefore, based on the AA Similarity Theorem, Traingle DEF ~ Triangle GDF.

Part C: Length of Segment ED

Given the following,

• EF = 8 (Hypotenuse)
• EG = 2 (Part)
• ED = ? (Leg)

Thus:

8/ED = ED/2 (Leg Rule)

• Cross multiply

ED² = (8)(2)

ED² = 16

• Find the square root of both sides

ED = 4

Learn more about AA Similarity Theorem on:

brainly.com/question/24147586