Mathematics, 16.08.2020 02:01 Bryson2148

Given: <2 and <4 are vertical angles. Prove: <2 ~= <4

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Given: <2 and <4 are vertical angles.

Prove: <2 ~= <4
Statements Reasons
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Answers: 3

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Answer from: princess42044

The proof of $\angle 2 \ and \ \angle4$ are vertical angles is explained below.

Given, $\angle 2 \ and \ \angle4$ are vertical angles as shown in fig.

We know that, Vertical angles are formed when two straight lines intersect at a point.Vertical angles are two angles which are vertically opposite and have the same measure. So, the two angles are to be congruent.

We have to prove that angle 2 and angle 4 congruent.

Given $\angle 2 \ and\ \angle 3$ makes linear pair so,

$\angle 2+\angle 3= 180$

$\angle 3 =180-\angle 2$ ..........(1)

Again $\angle 3 \ and \ \angle 4$ makes linear pair so,

$\angle 3+\angle 4= 180$

$\angle 3 =180-\angle 4$ .......(2)

From (1) and (2) we get,

$180-\angle 2=180-\angle 4$

Subtracting 180 from both the sides we get,

$-\angle 2=-\angle 4$

Or, $\angle 2=\angle 4$

Hence angle 2 and angle 4 are congruent.

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Answer from: jjuniorr

Statement 1: $\angle 2$ and $\angle 4$ are vertical angles

Reason 1: Given

We basically just restate the given information word for word. This is true of any two column proof.

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Statement 2: $m \angle 2 + m \angle 3 = 180$

Reason 2: $\angle 2$ and $\angle 3$ are a linear pair

The term "linear pair" means the angles are adjacent and supplementary (they form a straight line), so this is why the two angles add to 180.

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Statement 3: $m \angle 3 + m \angle 4 = 180$

Reason 3: $\angle 3$ and $\angle 4$ are a linear pair

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Statement 4: $m \angle 2 + m \angle 3 = m \angle 3 + m \angle 4$

Reason 4: Substitution

Each of the equations formed in statements 2 and 3 above have 180 on the right side, so the left hand sides must be the same

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Statement 5: $m \angle 2 = m \angle 4$

Reason 5: Subtraction property of equality

We subtracted the quantity $m \angle 3$ from both sides (they go away)

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Statement 6: $\angle 2 \cong \angle 4$

Reason 6: Definition of congruence

If two items are congruent, then they have the same measure. In other words, they are the same.

Answer from: Quest

when studying polynomials, you often hear the terms zeros, roots, factors and x x the multiplicity of a zero is important because it tells us how the graph of the let's look at the graph of a function that has the same zeros

step-by-step explanation:

Answer from: Quest

idk

step-by-step explanation:

58.35 what is the volume of the can below? use - 3.14 and round your answer to the nearest tenth. 8

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Given: <2 and <4 are vertical angles. Prove: <2 ~= <4

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