Question

What is the missing step in this proof?

Answer 1

Answer:

Option C is correct.

The missing steps in this proof is; $\angle 1 \cong \angle 4$ and $\angle 3 \cong \angle 5$.

Explanation:         

Given ΔABC.

Prove that:  The sum of the interior angle measures of ΔABC is $180^{\circ}$

Let A ,B and C forms a triangle    [Given]

Parallel lines are those two lines that are always the same distance apart and never touch.

then, by the definition of parallel lines and labeling angles

DE be the line passing through B, parallel to AC, with angles as labelled in the figure as shown below in the attachment.

Alternative Interior Angle theorem states that the angles that are formed on opposite sides of the transversal and inside the two lines are alternate interior angles also this theorem says that when the lines are parallel, then the alternate interior angles are equal.

Then,

$\angle 1 \cong \angle 4$ and                              

$\angle 3 \cong \angle 5$        [By Alternative Interior angle theorem]            

Angles are always congruent if their measures in degrees are equal.

therefore,

$m\angle 1 =m\angle 4$ and

$m\angle 3=m\angle 5$      [By Congruent Angle have equal measure]                                                                   ......[1]

Straight Angles states that angles on one side of a straight line always add to 180 degrees.

From the given figure;

By the addition angle and definition of straight angle we get;

$m\angle 4 +m\angle 2 +m\angle 5 =180^{\circ}$      ......[2]

Substituting equation [1] in [2] we get;

$m\angle 1 +m\angle 2 +m\angle 3 =180^{\circ}$  

Therefore, the sum of the interior angles measures of triangle ABC is $180^{\circ}$

Answer 2

The missing proof is the third statement

¹²³⁴⁵⁶⁷⁸⁹⁰⁹⁸⁷⁶⁵⁴³²¹
₁¹₁¹₁