Warm up:
The diagram below includes two squares: one has sides
of length 20 and the other has sides of length 10. What
is the area of the shaded region?
Area of shaded
region = 100
Similarity Proofs HMWK Answers
1)
Similarity Proofs HMWK Answers
2)
Similarity Proofs HMWK Answers
3)
Similarity Proofs HMWK Answers
4)
Similarity Proofs HMWK Answers
5)
Similarity Proofs HMWK Answers
6)
Hands on…
1) Get a pink ½ sheet of paper from the front.
2) Draw a line from 1 vertex to the opposite vertex.
3) Draw another line from either of the non-connected
vertices perpendicular to the 1st line drawn.
4) Cut out the 3 triangles and align them as shown.
What do you notice about the triangles?
We just demonstrated the following important
theorem about right triangles…
Right Triangle Altitude Theorem
In a rt. ∆, the altitude from the vertex of the right
angle to the hypotenuse forms 2 ∆’s that are
similar to the given ∆ and to each other.
Δ𝑃𝑄𝑅~Δ𝑃𝑆𝑄~Δ𝑄𝑆𝑅
Complete the following proof of the Rt. ∆ Altitude Thm.
Given: ∠𝑃𝑄𝑅 is a rt. ∠. 𝑄𝑆 is the altitude of Δ𝑃𝑄𝑅 drawn
from the rt. ∠.
Prove: Δ𝑃𝑆𝑄~Δ𝑃𝑄𝑅; Δ𝑄𝑆𝑅~Δ𝑃𝑄𝑅; Δ𝑃𝑆𝑄~Δ𝑄𝑆𝑅
Given: ∠𝑃𝑄𝑅 is a rt. ∠. 𝑄𝑆 is the altitude of Δ𝑃𝑄𝑅
drawn from the rt. ∠.
Prove: Δ𝑃𝑆𝑄~Δ𝑃𝑄𝑅; Δ𝑄𝑆𝑅~Δ𝑃𝑄𝑅; Δ𝑃𝑆𝑄~Δ𝑄𝑆𝑅
Given
Definition of altitude
Definition of perpendicular
Definition of right angle
Definition of congruent angles
Reflexive Prop. of Congruence
AA Similarity Thm.
Transitive Prop.
Geometric Means Theorems
Find x, y, and z.
X = 144
Y = 60
Z = 156
Find x, y, and z.
X = 20 3
Y = 10 21
Z = 20 7
The segments of the hypotenuse measure 4
inches and 16 inches.