Answer:
B
............................
Answer:
Δ QRS ≈ Δ QST ≈ Δ SRT ⇒ 3rd answer
Step-by-step explanation:
From the given figure
In Δ QRS
∵ m∠S = 90°
∵ m∠S = m∠QST + m∠RST
∴ m∠QST + m∠RST = 90° ⇒ (1)
- Use the fact the sum of the measures of the interior angles
of a Δ is 180°
∴ m∠Q + m∠S + m∠R = 180°
∵ m∠S = 90
∴ m∠Q + 90° + m∠R = 180°
- Subtract 90 from both sides
∴ m∠Q + m∠R = 90° ⇒ (2)
In Δ QST
∵ m∠QTS = 90°
- By using the fact above
∴ m∠Q + m∠QST = 90 ⇒ (3)
- From (1) and (3)
∴ m∠QST + m∠RST = m∠Q + m∠QST
- Subtract m∠QST from both sides
∴ m∠RST = m∠Q
In Δ SRT
∵ m∠STR = 90°
- By using the fact above
∴ m∠R + m∠RST = 90 ⇒ (4)
- From (1) and (4)
∴ m∠QST + m∠RST = m∠R + m∠RST
- Subtract m∠RST from both sides
∴ m∠QST = m∠R
In Δs QRS and QST
∵ m∠S = m∠QTS ⇒ right angles
∵ m∠R = m∠QST ⇒ proved
∵ ∠Q is a common angle in the two Δs
∴ Δ QRS ≈ Δ QST ⇒ AAA postulate of similarity
In Δs QRS and SRT
∵ m∠S = m∠STR ⇒ right angles
∵ m∠Q = m∠RST ⇒ proved
∵ ∠R is a common angle in the two Δs
∴ Δ QRS ≈ Δ SRT ⇒ AAA postulate of similarity
If two triangles are similar to one triangle, then the 3 triangles are similar
∵ Δ QRS ≈ Δ QST
∵ Δ QRS ≈ Δ SRT
∴ Δ QRS ≈ Δ QST ≈ Δ SRT
The measure of x is 100 degrees.
Explanation: a line is 180 degrees and we remove 80 from it because that’s the angle GFH, 180-80= 100 degrees
Answer:
706.5 ft²
Step-by-step explanation:
A. Width of the rectangle
The formula for the area of a rectangle is
A = lw
But, l = 3w, so,
A = (3w)w
= 3w² = 12
w² = 4 Divided each side by 3
w = 2 ft Took the square root of each side
B. Length of rectangle
l = 3w = 6 ft
C. Diameter of circle
d = 5l = 5 × 6 = 30 ft
D. Radius of circle
d = 2r
r = d/2 Divided each side by 2
r = 30/2 = 15 ft
E. Area of circle
A = πr² = 3.14 × 15² = 3.14 × 225 = 706.5 ft²
The area of the circle is 706.5 ft².
