Answer:
1. The similar triangles are ΔXYZ and ΔPQR
The triangles are similar by the AA rule of similarity
2. The similar triangles ΔXYZ and ΔPQR cannot be assumed as being congruent because more information are required about the length of a pair of corresponding sides of both triangles
3. x = 17.5
4. x = 20
Explanation:
1. The angles of triangle ΔXYZ are;
∠X = 32°, ∠Y = 84° and ∠Z = 180° - (84° + 32°) = 64°
The angles of triangle ΔPQR are;
∠P = 64°, ∠R = 32° and ∠Q = 180° - (64° + 32°) = 84°
The angles of triangle ΔABC are;
∠A = 64°, ∠C = 92° and ∠B = 180 - (92 + 64) = 24°
Therefore, the two similar triangles are ΔXYZ and ΔPQR
The triangles are similar based on Angle-Angle (AA) rule of similarity
2. The similar triangles ΔXYZ and ΔPQR cannot be assumed as being congruent because more information are required about the length of a pair of corresponding sides of both triangles
3. We have by corresponding triangles formed by the tree and Enzo as follows;
5 ft./(6 ft.)= x/(21 ft.)
∴ x = 21 ft.× (5 ft./6 ft.) = 17.5 ft.
x = 17.5 feet
4. By corresponding triangles, we have;
(35 ft.)/(40.5 ft.+ 54 ft.) = x ft./(54 ft.)
∴ x ft. = (54 ft.) × (35 ft.)/(40.5 ft.+ 54 ft.) = 54 ft. × (35 ft.)/(94.5 ft.) = 20 ft.
x ft. = 20 ft.
∴ x = 20