Proof is an art of convincing the reader that the given statement is true The proof techniques are chosen according to the statement that is to be proved Direct proof technique is used to prove implication statements which have two parts, an “if-part” known as Premises and a “then part” known as Conclusions

A formal proof of a statement is a sequence of steps that links the hypotheses of the statement to the conclusion of the statement using only deductive reasoningSolid Facts

1. Statement This states the theorem to be proved
2. Drawing This represents the hypothesis of the theorem
3. Given
4. Prove
5. Proof

Proofs are hard because we get exposed to them very late in our lives I find that many high-school students do not have any idea what a proof is For example, suppose I have to prove the following trivial statement: Prove that if is an odd number, then is an odd number

Line 5 shows the division property of equality The division property of equality states that you can divide both sides of the equation by the same number and the equation remains the same

The value of X will be 20 , Hope this helps !

The missing reason in the proof is Transitive property

Answer Expert Verified The correct answer is: The fourth diagram Explanation: The fourth diagram has two same-side interior angles that are supplementary (add to 180°)

Answer Expert Verified Thus, since both the angles, and have equal values or equal measures, both amounting to Therefore, by definition of congruent angles, / Thus, the missing reason in the proof at step #8 is “definition of congruent angles”

The correct statement which is true about angle 3 and 5 is, they are supplementary Step-by-step explanation: Two parallel lines are intersected by a third line so that angles 1 and 5 are congruent as they are supplementary Supplementary Angles are Supplementary when the two angles are add up to 180 degrees

“Angle H E G is 2 and angle G E F is 1” Meaning that another name for angle 1, is G E F

Parallel lines are lines in a plane that are always the same distance apart Parallel lines never intersect Perpendicular lines are lines that intersect at a right (90 degrees) angle

The correct answer is it must be a right angle Explanation: This is a rhombus, as it is a parallelogram with all congruent sides In a rhombus, diagonals are perpendicular bisectors of each other; this means that they meet at right angles, so MSR must be a right angle

We have now proven that all three angles of ΔABC have a measure of 60 degrees Therfore, ∠C must have a measure of 60 degrees

An angle of 90 degrees, as in a corner of a square or at the intersection of two perpendicular straight lines You just studied 11 terms!

So, 60° is the answer

The size of an angle is measured in degrees (see Angle Measures) When we say ‘the angle ABC’ we mean the actual angle object If we want to talk about the size, or measure, of the angle in degrees, we should say ‘the measure of the angle ABC’ – often written m∠ABC However, many times we will see ‘∠ABC=34°’

What is true about the measure of angle B? It is equal to the measure of angle C

The measure of B would be 60 degrees This means that the triangle is an equalateral triangle, and since all triangles interior angles equal 180 degrees,

So: Thus, angle B is 108 degrees

Draw a vertical line connecting the 2 rays of the angle To determine the number of degrees in an acute angle, connect the 2 rays to form a triangle Line up the short end of your ruler with the bottom ray, then draw a vertical line intersecting the other ray using the long side of your ruler