1- Finish the following proof.   Given: angle 4 is congruent to angle 5 Prove: m angle 2+ m angle 3 = 90 degrees Statements                                            ...

1- Finish the following proof.  

Given: angle 4 is congruent to angle 5

Prove: m angle 2+ m angle 3 = 90 degrees

Statements                                              Reasons

a.  ?                                                         a. Given

b.  a perpendicular to b                               b.  ?

c.  ?                                                          c.  ?

d. m angle 2+ m angle 3 = 90 degrees          d.  ?

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embizze's profile pic

embizze | High School Teacher | (Level 1) Educator Emeritus

Posted on

1) `/_4 cong /_5 ` ,diagram as given        1) Given

2) `a _|_ b `                                             2) If two lines meet to form congruent adjacent angles, then the lines

                                                             are perpendicular.

3) `/_2 ` is complementary to `/_3 `          3) If the exterior sides of two adjacent angles are perpendicular, then the angles are complementary.

4) `m/_2+m/_3=90 `                  4) Definition of complementary angles

Note that angles 4 and 5 are adjacent as they share a common vertex, a common side, and have no interior points in common. Also, angles 2 and 3 are adjacent for the same reasons. The exterior sides of angles 2 and 3 (the sides that are not shared) are the rays formed by lines a and b.

llltkl's profile pic

llltkl | College Teacher | (Level 3) Valedictorian

Posted on

Given: angle 4 is congruent to angle 5

Prove: m angle 2+ m angle 3 = 90 degrees

Statements                                    Reasons

a. <4 is congruent to <5                 a. Given.

b.  a perpendicular to b                   b. <4 and <5 form a linear pair, m<4=m<5=`90^o` ,

                                                          a intersects b at right angles.

c. m<4=m<2+m<3=`90^o`                c. Vertically opposite angles.                                           

d. m<2+m<3=`90^o`                         d. Complementary adjacent angles.

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