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GR + RE = GE
Segment Addition Postulate
If R is the midpoint of GE, then RE = ½ GE.__
Midpoint Theorem
If RA RD, then ARD is a right
angle.
↔ ↔
Def. of Perpendicular Lines
If GRC is supplementary to ARC, and DRF is
supplementary to ARC, then GRC DRF.
Congruent Supplements Theorem
GRB ERF
Vertical Angles Are Congruent.
If RC bisects BRD, then mBRC = ½ mBRD.
→
Angle Bisector Theorem
mGRA + mARC = mGRC.
Angle Addition Postulate
If BF GE, then
GRB BRE.
↔ ↔
If two lines are perpendicular, then they form congruent adjacent
angles.
If mERD + mCRA = 90, then those angles are
complementary.
Definition of Complementary Angles
If BR RF, then R is the midpoint of BF.
__ ____
Definition of Midpoint
If RB RE, then BRC is complementary to
CRE.
→ →
If the exterior sides of two adjacent acute angles are perpendicular, then the
angles are complementary.
If GRA is supplementary to FRD, then mGRA +
mFRD = 180.
Definition of Supplementary Angles
If R is the midpoint of GE, then FB bisects GE.
↔
____
Definition of Segment Bisector
If BRE ERF, then EG FB.↔ ↔
If two lines form congruent adjacent angles,
then the lines are perpendicular.
mARB + mBRC = mARC
Angle Addition Postulate
If BR RF, then R is the midpoint of BF.
__ ____
Definition of Midpoint
If mARD = 90, then ARD is a right angle.
Definition of Right Angle
If ARD is a right angle, then RA RD.
→ →
Definition of Perpendicular Lines
If FB GE, then
BRE ERF.
↔ ↔
If two lines are perpendicular, then they form congruent adjacent
angles.
If ARB is complementary to BRD,
and DRE is complementary to BRD,
then ARB DRE.
Congruent Complements Theorem
If RC bisects BRD, then BRC CRD.
→
Definition of Angle Bisector
mGRC + mCRE = 180
Linear Pair Postulate
If BRG BRE, then BR GE.↔ ↔
If two lines form congruent adjacent angles,
then the lines are perpendicular.
FR + RB = FB
Segment Addition Postulate
If RB RE, then BRD and DRE are
complementary.
→ →
If the exterior sides of two adjacent acute angles are perpendicular, then the
angles are complementary.
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