**Disclaimer: When you are completing full proofs you may not always need to use each given or necessarily go as far as you need to on this page.
- m1 = m2GIVEN
- m1 + m5 = 90 degreesGIVEN
- 1 and 7 form a linear pairGIVEN
- 8 is a rt angle and 9 is a rt angleGIVEN
- 4 and 7 are complementaryGIVEN
- 1 7 GIVEN
- m1 +m 4 = 180 degreesGIVEN
- 8 and 9 are vertical anglesGIVEN
- 3 and 8 are supp. anglesGIVEN
- 8 and 10 are both complementary to 7GIVEN
- 1 and 2 are supplementaryGIVEN
- 1 and 5 are supplementaryGIVEN
13. ABC is a right angleGIVEN
- DB = SGGIVEN
- H and P form a linear pairGIVEN
- =GIVEN
- mABC = 147; mJLM = 147 GIVEN
- TI = FG, FG = SDGIVEN
- DMB is a right angleGIVEN
- 3 and 7 are comp;
6 and 7 are compGIVEN
- QWE and MNB are supp;
WSZ and MNB are suppGIVEN
- m 7 = 30 ; m 8 = 30 GIVEN
- 1 8GIVEN
- AB = DC; DC = EF; EF =GH; GH =IJGIVEN
- MJR is a rt angle;
TUV is a rt angleGIVEN
- m1 = m2GIVEN
12 / Definition of Congruent Angles
(Congruent angles - Angles that have the same measure.)
- m1 + m5 = 90 degreesGIVEN
1 and 5 are complementary angles / Definition of Complementary Angles
(Complementary Angles-Two angles whose measures have a sum of 90 degrees.)
- 1 and 7 form a linear pairGIVEN
1 and 7 are supplementary angles / Linear Pair Theorem
(LPT-If two angles form a linear pair then they are supplementary.)
m1 + m7 = 180 degrees / Definition of Supplementary Angles
(Supplementary Angles-Two angles whose measures have a sum of 90 degrees.)
- 8 is a rt angle and 9 is a rt angleGIVEN
8 9 / Right Angle Congruence Theorem
(RACT-All right angles are congruent.)
m8 = m9 / Definition of Congruent Angles
(Congruent angles - Angles that have the same measure.)
- 4 and 7 are complementaryGIVEN
m4 + m7 = 90 degrees / Definition of Complementary Angles
(Complementary Angles-Two angles whose measures have a sum of 90 degrees.)
- 1 7 GIVEN
m1 = m7 / Definition of Congruent Angles
(Congruent angles - Angles that have the same measure.)
- m1 + m 4 = 180 degreesGIVEN
1 and 4 are supplementary angles / Definition of Supplementary Angles
(Supplementary Angles-Two angles whose measures have a sum of 90 degrees.)
- 8 and 9 are vertical anglesGIVEN
89 / Vertical Angles Theorem
(VAT-Vertical Angles are Congruent.)
m8 = m9 / Definition of Congruent Angles
(Congruent angles - Angles that have the same measure.)
- 3 and 8 are supp. anglesGIVEN
m3 +m8 = 180 degrees / Definition of Supplementary Angles
(Supplementary Angles-Two angles whose measures have a sum of 90 degrees.)
- 8 and 10 are both supplementary to 7GIVEN
8 10 / Congruent Supplements Theorem
(CST-If two angles are supplementary to the same angle then the two angles are congruent.)
- 1 and 2 are supplementaryGIVEN
m1 + m2 = 180 degrees / Definition of Supplementary Angles
(Supplementary Angles-Two angles whose measures have a sum of 90 degrees.)
- 1 and 5 are supplementaryGIVEN
m1 + m5 = 180 degrees / Definition of Supplementary Angles
(Supplementary Angles-Two angles whose measures have a sum of 90 degrees.)
- ABC is a right angleGIVEN
mABC = 90 degrees / Definition of a right angle
(Right Angle- An angle that measures 90 degrees)
- DB = SGGIVEN
/ Definition of congruent segments
(Congruent Segments- Segments that have the same length.)
- H and P form a linear pairGIVEN
H and P are supplementary / Linear Pair Theorem
(LPT-If two angles form a linear pair then they are supplementary.)
mH + mP = 180 degrees / Definition of Supplementary Angles
(Supplementary Angles-Two angles whose measures have a sum of 90 degrees.)
- GIVEN
MA = TH / Definition of Congruent Segments
(Congruent Segments- Segments that have the same length.)
- mABC = 147 degrees;
mJLM = 147 degreesGIVEN
mABC = mJLM / Transitive property of Equality
(If a = b and b= c then a = c)
(Technically could be substitution also)
ABC JLM / Definition of Congruent Angles
(Congruent angles - Angles that have the same measure.)
- TI = FG, FG = SDGIVEN
TI = SD / Transitive property of Equality
(If a = b and b= c then a = c)
- DMB is a right angleGIVEN
mDMB = 90 degrees / Definition of a right angle
(Right Angle- An angle that measures 90 degrees)
- 3 and 7 are comp;
6 and 7 are compGIVEN
3 6 / Congruent Complements Theorem
(CCT-If two angles are complementary to the same angle then the two angles are congruent.)
m3 = m6 / Definition of Congruent Angles
(Congruent angles - Angles that have the same measure.)
- QWE and MNB are supp;
WSZ and MNB are suppGIVEN
QWEWSZ / Congruent Supplements Theorem
(CST-If two angles are supplementary to the same angle then the two angles are congruent.)
mQWE = mWSZ / Definition of Congruent Angles
(Congruent angles - Angles that have the same measure.)
- m 7 = 30 degrees
m 8 = 30 degreesGIVEN
m7 = m8 / Transitive Property of Equality
(If a = b and b= c then a = c)
(Technically this could be substitution also)
7 8 / Definition of Congruent Angles
- 1 8GIVEN
m1 = m8 / Definition of Congruent Angles
(Congruent angles - Angles that have the same measure.)
- AB = DC; DC = EF; EF =GH; GH =IJGIVEN
AB = IJ / Transitive Property of Equality
(If a = b and b= c then a = c)
- MJR is a rt angle;
TUV is a rt angleGIVEN
MJR TUV / Right Angle Congruence Theorem
(RACT-All right angles are congruent.)
mMJR = mTUV / Definition of Congruent Angles
(Congruent angles - Angles that have the same measure.)