If <3 is congruent to <4,prove that <3 and <4 are right angles.
LOL, without a drawing there is no way. Perhaps they add up to a straight line?
Yes they do add up to a straight line with a bisector making each angle equal to 90 degrees
well then 90 degrees is 1/4 circle, straight line is 1/2
1/4 = 1/2 of 1/2
To prove that angle <3 and angle <4 are right angles, we need to use the given information that <3 is congruent to <4.
Here's the step-by-step explanation:
Step 1: Start by assuming that angle <3 is not a right angle.
Step 2: Since angle <3 is congruent to angle <4, we know that the measures of both angles are equal.
Step 3: Let's assign the measure of angle <3 as "x". Therefore, the measure of angle <4 is also "x".
Step 4: Since angle <3 is not a right angle, its measure is less than 90 degrees. Therefore, 0 < x < 90.
Step 5: Since angle <3 and angle <4 have the same measure, angle <4 is also restricted to the same range: 0 < x < 90.
Step 6: Now, consider that if angles <3 and <4 are not right angles, their measures can only be between 0 and 90 degrees.
Step 7: In this case, if angle <3 = angle <4 = x, where 0 < x < 90, then the possible ranges of x will be overlapping.
Step 8: However, if we draw two overlapping angles within the range of 0 to 90 degrees, it is not possible for them to be congruent.
Step 9: Therefore, there is a contradiction with our assumption that <3 is not a right angle.
Step 10: Hence, we can conclude that if angle <3 is congruent to angle <4, then both <3 and <4 must be right angles.
Therefore, by using proof by contradiction, we have shown that if <3 is congruent to <4, then both <3 and <4 are right angles.