Find the volume of the triangular prism described below.
1 answer:
The volume of the prism 121.6 cube in.
Step-by-step explanation:
Given,
The base is right angle triangle whose two sides are equal.
So,
Base (b) = 8 in
Another side of right angle triangle (l) = 8 in
Height (h) of the prism = 3.8 in
To find the volume of the prism.
Formula:
V = bhl
Now,
V = ×8×8×3.8 cube in
= 121.6 cube in.
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- 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.
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
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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.
