Mathematics, 16.08.2020 02:01, Bryson2148

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

Statements Reasons

Assemble the proof by dragging tiles to
the Statements and Reasons columns

Given: <2 and <4 are vertical angles.

Prove: <2 ~= <4
Statements Reasons
Assemble the

Answers: 3

Show answers

Answers

answered: 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.

For more details follow the link:

link

answered: 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.

-------------------------------------

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.

--------------------------------------

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

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

--------------------------------------

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

--------------------------------------

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)

--------------------------------------

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.

answered: Guest

y = 2x

step-by-step explanation:

if you divide each number in the sequence, you'll see that they all have a multiple factor of 2. each number in the series, and any other numbers which may continue, will be multiplied by 2. therefore, y is the next number in the sequence, and x is the current one, so, our formula will be y = 2x.

answered: Guest

Where is the qeustion

Other questions on the subject: Mathematics

Mathematics, 21.06.2019 14:30, azaz1819

Geometry: determine whether segment mn is parallel to segment kl. justify your answer. jm 6 mk 3 jn 8 nl 4

Answers: 3

continue

Mathematics, 21.06.2019 19:30, mya1318

Acourt reporter is transcribing an accident report from germany. the report states that the driver was traveling 80 kilometers per hour. how many miles per hour was the driver traveling?

Answers: 2

continue

Mathematics, 21.06.2019 20:30, anispotts

If a 36 inch yardstick casts a 21 foot shadow, how tall is a building whose shadow is 168 feet? what is the scale factor

Answers: 1

continue

Mathematics, 21.06.2019 21:00, 22MadisonT

Abakery recorded the number of muffins and bagels it sold for a seven day period. for the data presented, what does the value of 51 summarize? a) mean of bagels b) mean of muffins c) range of bagels d) range of muffins sample # 1 2 3 4 5 6 7 muffins 61 20 32 58 62 61 56 bagels 34 45 43 42 46 72 75

Answers: 2

continue

Do you know the correct answer?

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

Statements Reasons