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.
Answers
Match the remaining steps to their correct sequence in the proof.
Step-by-step explanation:
Given,
∆ABC with m∠ABC = 90°
To prove;
Proof;
Statement - Reason
1). Draw BD ⊥ AC - Construction
2). ∠ABC ≅ ∠BDC - Angles with the same measure are congruent.
3). ∠BCA ≅ ∠DCB - Reflexive Property of Congruence
4). ∆ABC ≈ ∆BDC - AA criterion for similarity
5). BC/DC = AC/BC - Corresponding sides of similar triangles are proportional.
6). BC^2 = AC × DC - cross multiplication
7). ∠ABC ≅ ∠ADB - Angles with the same measure are congruent.
8). ∠BAC ≅ ∠DAB - Reflexive Property of Congruence
9). ∠ABC ≈ ∠ADB - AA criterion for similarity
10). AB/AD = AC/AB - Corresponding sides of similar triangles are proportional.
11). AB^2 = AC * AD - Cross multiplication
12). AB^2 + BC^2 = AC(AD + DC) - Distributive property
13). AB^2 + BC^2 = AC * AC - segment addition
14). AB^2 + BC^2 = AC^2 - Mulitplication
Learn more: Pythagoras theorem
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