Drag the tiles to the correct boxes to complete the pairs. The figure shows ∆ABC with m∠ABC = 90°. The first 10 steps to prove t
hat AB2 + BC2 = AC2 are given in the table. Match the remaining steps to their correct sequence in the proof. Statement Reason 1. Draw . construction 2. ∠ABC ≅ ∠BDC Angles with the same measure are congruent. 4. ∠BCA ≅ ∠DCB Reflexive Property of Congruence 4. AA criterion for similarity 5. Corresponding sides of similar triangles are proportional. 6. BC2 = AC × DC cross multiplication 7. ∠ABC ≅ ∠ADB Angles with the same measure are congruent. 8. ∠BAC ≅ ∠DAB Reflexive Property of Congruence 9. AA criterion for similarity 10. Corresponding sides of similar triangles are proportional. 11. 12. 13. 14. 15. AB2 + BC2 = AC2 Reason: multiplication AB2 + BC2 = AC × AC Reason: segment addition AB2 = AC × AD Reason: cross multiplication AB2 + BC2 = AC(AD + DC) Reason: Distributive Property AB2 + BC2 = AC × AD + AC × DC Reason: addition
2 answers:
Answer:
Drag the tiles to the correct boxes to complete the pairs.
The figure shows ∆ABC with m∠ABC = 90°.
The first 10 steps to prove that AB2 + BC2 = AC2 are given in the table. Match the remaining steps to their correct sequence in the proof.
Statement Reason
1. Draw . construction
2. ∠ABC ≅ ∠BDC Angles with the same measure are congruent.
4. ∠BCA ≅ ∠DCB Reflexive Property of Congruence
4. AA criterion for similarity
5. Corresponding sides of similar triangles are proportional.
6. BC2 = AC × DC cross multiplication
7. ∠ABC ≅ ∠ADB Angles with the same measure are congruent.
8. ∠BAC ≅ ∠DAB Reflexive Property of Congruence
9. AA criterion for similarity
10. Corresponding sides of similar triangles are proportional.
11.
12.
13.
14.
15.
AB2 + BC2 = AC2
Reason: multiplication
AB2 + BC2 = AC × AC
Reason: segment addition
AB2 = AC × AD
Reason: cross multiplication
AB2 + BC2 = AC(AD + DC)
Reason: Distributive Property
AB2 + BC2 = AC × AD + AC × DC
Reason: addition
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Step-by-step explanation:
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ANSWER
<em>alternate interior angles theorem</em>
EXPLANATION
According to the alternate interior angles theorem, when two parallel lines are are intercepted by a straight line (transversal) the angles in the interior corners of a Z-shape pattern are congruent.
From the above diagram line r is parallel to line s, therefore
and
because they are alternate interior angles.
See attachment for how to spot alternate interior angles.
