- Angle 1 is congruent to angle 2, since BD bisects <ABC and the two angles created on each side of the bisector at point B are equal.
- <2 ≅ <3 because of the corresponding angles theorem.
- <1 ≅ <4 because alternate angles are congruent if two parallel lines are cut by a transversal.
- <3 ≅ <4 by the substitution property of equality.
- AD/CD = EB/CB by the triangle proportionality theorem.
- If two angles in a triangle are congruent, the sides opposite the angles are congruent, so AE = EB.
- AD/CD = AB/CB by the substitution property of equality.
<h3>The properties of similar triangles.</h3>
In Geometry, two (2) triangles are said to be similar when the ratio of their corresponding side lengths are equal and their corresponding angles are congruent.
<h3>What is the substitution property of equality?</h3>
The substitution property of equality states that assuming x, y, and z are three (3) quantities, and if x is equal to y (x = y) based on a rule and y is equal to z (y = z) by the same rule, then, x and z (x = y) are equal to each other by the same rule.
In this context, we can reasonably infer and logically deduce that the ratio of AD/CD is equal to AB/CB based on the substitution property of equality.
Read more on substitution property here: brainly.com/question/2459140
#SPJ1
Complete Question:
In ΔABC, side BC is extended to point E. When connected to vertex A, segment EA is parallel to segment BD. In this construction, you are given that BD bisects <ABC.
Prove: AD/CD = AB/CB.
Complete the paragraph proof.
You have to use the Law of Cosines here, since there's no other way to solve this. it's not a right triangle, so you can't use the Pythagorean Theorem. The Law of Cosines will help us find the missing side length then we will have to use the Law of Sines to find another angle. Then after that we will use the Triangle Angle-Sum theorem to finish it off. Ready? The Law of Cosines to find side b is

and fill in the info we know, which is everything but the b.

. Doing all that math gives us that side b = 40.9 or 41. Now the Law of Sines to find missing angle A or C. Let's find A.

. That gives us that angle A is 29. Now use the fact that all triangles add up to 180 to get that angle C is 42. And you're done!
20:12
i think. 20 being the number of total students to 12 which is the number of boys
Answer:
False
Step-by-step explanation:
f(x) = 4x³ - 12x² - x + 15
Set output to 0.
Factor the function.
0 = (x + 1)(2x - 3)(2x - 5)
Set factors equal to 0.
x + 1 = 0
x = -1
2x - 3 = 0
2x = 3
x = 3/2
2x - 5 = 0
2x = 5
x = 5/2
-2 is not a lower bound for the zeros of the function.
Answer:
x = -1/2
Step-by-step explanation:
4(x + 3) = 9x + 16 + 3x
Distribute the 4
4x +12 = 9x+16+3x
Combine like terms
4x+12 = 12x+16
Subtract 4x
4x-4x+12 = 12x-4x+16
12 = 8x+16
Subtract 16
12-16 = 8x+16-16
-4 =8x
Divide by 8
-4/8 =8x/8
-1/2 =x