Given: ST = RN; IT = RU Prove: SI = UN1. ST = RN 1. 2. 2. 3. SI + IT = RU + UN 3. 4. IT = RU 4. 5. 5. StatementsReasonsST = SI + ITRN = RU + UNSI = UNGivenSegment Add. Post.SubstitutionGivenSubtraction Prop.SITRUN
Postulate A statement accepted without proof.Theorem A statement that can be proven using other definitions, properties, and postulates.In this class, we will prove many of the Theorems that we will use.
If M is the midpoint of AB, then AM = AB and MB = AB. Hypothesis: M is the midpoint of ABConclusion: AM = AB and MB = AB Write these pieces of the conditional statement as your given and prove information.Given:Prove:
Definition of Midpoint: the point that divides a segment into two congruent segments.Midpoint Theorem: If M is the midpoint of AB, then AM = AB and MB = AB. The theorem proves properties not given in the definition.
Proof of the Midpoint TheoremGiven: M is the midpoint of ABProve: AM = AB; MB = AB 184.108.40.206.220.127.116.11.18.104.22.168.M is the midpoint of ABMB = AB AM = MB AM + MB = AB AM + AM = AB 2AM = ABAM = ABGivenDef. of a MidpointSegment Add. Post.SubstitutionDivision PropertySubstitution
If BX is the bisector of ABC, then mABX = mABC and mXBC = mABC. Prove: mABX = mABC and mXBC = mABC.
A ray that divides an angle into two congruent adjacent angles.XWY @YWZIf WY is the bisector of XWZ, then mXWY = mXWZ and mYWZ = mXWZ.
Proof of the Bisector ThmProve: mABX = mABC and mXBC = mABC. Given: BX is the bisector of ABC.X1. Given2. mABX = mXBC2. Def. of an angle bisector3. mABX + mXBC = mABC3. Angle Addition Postulate4. mABX + mABX = mABC 2mABX = mABC4. Substitution5. mABX = mABC 5. Division Property 6. mXBC = mABC 6. Substitution