Mathematical Proofs: Practice (Edmentum)

Select the correct answer from each drop-down menu. Bobby and Elaine each write a proof for the statement m∠DCB=95∘. Given: m∠ACD=85∘ Prove: m∠DCB=95∘ Bobby's Proof: By the linear pair theorem, ∠ACD is supplementary to ∠DCB. This means that m∠ACD+m∠DCB=180∘. Since m∠ACD=85∘, the substitution property of equality implies that 85∘+m∠DCB=180∘. Applying the subtraction property of equality, m∠DCB=95∘. Elaine's Proof: Suppose m∠DCB≠95∘. By the linear pair theorem, ∠ACD is supplementary to ∠DCB. This means that m∠ACD+m∠DCB=180∘. Using the substitution property of equality, this means that m∠ACD+95∘≠180∘. Applying the subtraction property of equality, m∠ACD≠85∘. Since this contradicts what is given, then m∠DCB=95∘. What type of proofs did they use?

Bobby used (a direct proof) because (each statement follows logically from the previous statement) . Elaine used (an indirect proof) because (the final statement is an impossibility) (Shoutout to o0011lez on Brainly for this one)

Given: ∠ACD≅ ∠XYZ Prove: ∠XYZ is supplementary to ∠DCB Which statement in the proof is not correctly supported?

Statement 3, because the transitive property applies only to congruence and equality.

Prove: Intersecting line segments always form 2 pairs of vertical angles. Which image provides a counterexample to disprove this statement?

XOB

Drag each label to the correct location on the chart. Given: angle ADC ≌ angle BDC Prove: mangle BDC=90 ° raw the proof in a flow chart. sear noir thesren definition of supplementary angle ADC ≌ angle BDC mangle ADC=mangle BDC substitution property of equality division propenty of equality gives de nnition of cosgruence mangle BDC=180 ° mangle BDC=90 ° 2mangle BDC=180 ° angle ADC his complementary angle BDC 1o mangle ADC+ angle ADC 18 sucele: me vitary mangle BDC=180 ° to angle BDC

https://www.gauthmath.com/solution/1773762302684166/Question-1-of-5-Drag-each-label-to-the-correct-location-on-the-chart-Given-angle

By the linear pair theorem, ∠2 is supplementary to ∠3, which means m∠2 +m∠3=180∘. It is given that ∠3≅ ∠4, so by the definition of congruent angles, m∠3=m∠4. Using the substitution property of equality, substitute m∠4 in for m∠3 to rewrite the previous equation as m∠2+m∠4=180∘. Thus ∠2 is supplementary to ∠4 by the definition of supplementary angles. By the linear pair theorem, ∠1 is supplementary to ∠4. Since ∠2 and ∠1 are supplementary to ∠4, then by the congruent supplements theorem, ∠1≅ ∠2. Use the paragraph proof to complete the two-column proof. What statement and reason belong in line 5?

the angle sum of 2 and 4 is 180 degrees; substitution property of equality