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.
<em><u>Recall:</u></em>
- 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.
<em><u>Part A: A Pair of Similar Triangles</u></em>
A pair of similar triangles are traingle DEF and triangle GDF
<em><u>Part B: Reason for Similarity</u></em>
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.
<em><u>Part C: Length of Segment ED</u></em>
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:
