We have to prove that rectangles are parallelograms with congruent Diagonals.
Solution:
1. ∠R=∠E=∠C=∠T=90°
2. ER= CT, EC ║RT
3. Diagonals E T and C R are drawn.
4. Shows Quadrilateral R E CT is a Rectangle.→→[Because if in a Quadrilateral One pair of Opposite sides are equal and parallel and each of the interior angle is right angle than it is a Rectangle.]
5. Quadrilateral RECT is a Parallelogram.→→[If in a Quadrilateral one pair of opposite sides are equal and parallel then it is a Parallelogram]
6. In Δ ERT and Δ CTR
(a) ER= CT→→[Opposite sides of parallelogram]
(b) ∠R + ∠T= 90° + 90°=180°→→→Because RECT is a rectangle, so ∠R=∠T=90°]
(c) Side TR is Common.
So, Δ ERT ≅ Δ CTR→→[SAS]
Diagonal ET= Diagonal CR →→→[CPCTC]
In step 6, while proving Δ E RT ≅ Δ CTR, we have used
(b) ∠R + ∠T= 90° + 90°=180°→→→Because RECT is a rectangle, so ∠R=∠T=90°]
Here we have used ,Option (D) : Same-Side Interior Angles Theorem, which states that Sum of interior angles on same side of Transversal is supplementary.
Answer:
x=45degrees because there is 180 degrees on the straight lne and the first one is 90 degeeese and since it is split in half 90/2 is 45
Step-by-step explanation:
Well well we find the area of the triangle first:
area = 1/2 * base * height
area = 1/2 * 8 1/4 * 5 3/4
area = 1/2 * 33/4 * 23/4
area = 1/2 * 759/16
area = 759 / 32
area = 23 23/32
now if we multiply the length of the triangles we get volume because the volume of the prism is really just the sum of the areas of all the triangles that make up it's length. So:
volume = 23 23/32 * 12
volume = 276 276/32
276/ 32 = 8 5/8
volume = 284 5/8
Answer:
The answer is 4.
Step-by-step explanation:
8/3 ÷ 2/3 = 8/3 x 3/2 = 4
Answer:
Option A.
Step-by-step explanation:
Distance between Bob and the center of the mountain at the base = 19,427.5 ft.
Angle of elevation to the top of the mountain = 25°11'
We know that
1 degree = 60 minutes
1/60 degree = 1 minute
Let the height of the mountain be h.
In a right angled triangle
Therefore, the height of the mountain to the nearest foot 9135. Option A is correct.
