Answer: AA similarity theorem.
Step-by-step explanation:
Given : AB ∥ DE
Prove: ΔACB ≈ ΔDCE
We are given AB ∥ DE. Because the lines are parallel and segment CB crosses both lines, we can consider segment CB a transversal of the parallel lines. Angles CED and CBA are corresponding angles of transversal CB and are therefore congruent, so ∠CED ≅ ∠CBA.
Also ∠C ≅ ∠C using the reflexive property.
Therefore by AA similarity theorem , ΔACB ≈ ΔDCE
- AA similarity theorem says that if in two triangles the two pairs of corresponding angles are congruent then the triangles are similar .
Detailed Answers:
Volume of a Sphere (V) = 4/3 πr^3
1. Diameter (d) = 21.6 cm
Radius (r) = 21.6/2 = 10.8 cm
Therefore,
= 4/3 πr^3
= 4/3 * 22/7 * (10.8)^3
= 4/3 * 22/7 * 1259.712
= 88/21 * 1259.712
=> 5278.79
Volume (V) = 5278.79 cm^3
2. Diameter (d) = 16 cm
Radius (r) = 16/2 = 8 cm
Therefore,
= 4/3 πr^3
= 4/3 * 22/7 * (8)^3
= 4/3 * 22/7 * 512
= 88/21 * 512
=> 2145.52
Volume (V) = 2145.52 cm^3
3. Diameter (d) = 24 cm
Radius (r) = 24/2 = 12 cm
Therefore,
= 4/3 πr^3
= 4/3 * 22/7 * (12)^3
= 4/3 * 22/7 * 1728
= 88/21 * 1728
=> 7241.14
Volume (V) = 7241.14 cm^3
4. Diameter (d) = 6 cm
Radius (r) = 6/2 = 3 cm
Therefore,
= 4/3 πr^3
= 4/3 * 22/7 * (3)^3
= 4/3 * 22/7 * 27
= 88/21 * 27
=> 113.14
Volume (V) = 113.14 cm^3
Angle A would be 40 degrees I’m sure because it is a rotation not a dilation (which changes the measurements including the lengths and degree of angles)
Hope I helped :)
Answer:
0.0000571
Step-by-step explanation:
Height after 9th bounce = Initial height * (19/100)^9
= 177*(0.19)^9
= 0.00005711572
Answer:
n = -15
Step-by-step explanation:
Represent the number by n.
Then 2(n + 6) = n - 3
Performing the indicated multiplication, we get:
2n + 12 = n - 3
Combining like terms, we get n = -15