The theorems that matches each respective description are:
- Vertical Angles Theorem - 1
- Triangle Sum Theorem - 2
- Corresponding Angles Postulate - 5
- Same-Side Interior Angles Theorem - 8
- Isosceles Triangle Theorem - 3
- Alternate Exterior Angles Theorem - 7
- Triangle Midsegment Theorem - 4
- Alternate Interior Angles Theorem - 6
<h3>What is the Vertical Angles Theorem?</h3>
- This theorem states that a pair of vertical angles that are formed will always be congruent.
- Number 1 description matches this theorem.
<h3>What is the Triangle Sum Theorem?</h3>
- This states that all three interior angles of a triangle equals 180 degrees.
- Number 2 description matches this theorem.
<h3>What is the Corresponding Angles Postulate?</h3>
- This states that the corresponding angles formed, when a transversal cuts two parallel lines, are congruent.
- Number 5 description matches this theorem.
<h3>What is the Same-Side Interior Angles Theorem?</h3>
- This states that the same-side interior angles formed, when a transversal cuts two parallel lines, are congruent.
- Number 8 description matches this theorem.
<h3>What is the Isosceles Triangle Theorem?</h3>
- This states that the the two equal sides of an isosceles triangle are directly opposite the two congruent angles of the triangle.
- Number 3 description matches this theorem.
<h3>What is the Alternate Exterior Angles Theorem?</h3>
- This states that the alternate exterior angles formed, when a transversal cuts two parallel lines, are congruent.
- Number 7 description matches this theorem.
<h3>What is the Triangle Midsegment Theorem?</h3>
- This states that the midsegment of a triangle is always half the length of the third side it is parallel to.
- Number 4 description matches this theorem.
<h3>What is the Alternate Interior Angles Theorem?</h3>
- This states that the alternate interior angles formed, when a transversal cuts two parallel lines, are congruent.
- Number 6 description matches this theorem.
Learn more about Angles Theorem on:
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Answer:
-2 = n
Step-by-step explanation:
-3 + 4n = 4n + 3 + 3n
-3 + 4n = 7n + 3 [Combine like-terms]
-7n -7n
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-3 - 3n = 3
+3 +3
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-3n = 6
n = -2
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Answer:
0.26
Step-by-step explanation:
I am pretty sure the equation for this is 9x12+108 inches then divide 28.08 by 108 and you should get 0.26.
Answer:
Length = Width = Height = 64 ; Luggage Box is a CUBE
Step-by-step explanation:
Given : Length (L) + Width (W) + Height (H) ≤ 192 ; & Length = Width
Volume ( V )of luggage [Cuboid] = L.W.H
Since L = W :
V = L.L.H → V = L^2H
L + L + H = 192 → 2L + H = 192 → H = 192 - 2L
Putting value of 'H' in 'V'
V = L^2 (192 - 2L) → V = 192L^2 - 2L^3
Maximising volume function , differentiating it w.r.t 'L'
dV / dL = 2(192 L) - 3 (2L^2) → = 384L - 6L^2
dV / dL = 384L - 6L^2 = 0
384L = 6L^2 → 384 = 6L
L = 384 / 6 → L = 64 ; W also = 64
Putting value of L in 1st given sum equation : 2L + H = 192
2 (64) + H = 192
128 + H = 192 → H = 192 - 128 → H = 64
Since L = W = H = 64 ; Luggage bag is a Cube
