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:
Options (3) and (6)
Step-by-step explanation:
ΔABC is a dilated using a scale factor of to produce image triangle ΔA'B'C'.
Since, dilation is a rigid transformation,
Angles of both the triangles will be unchanged or congruent.
m∠A = m∠A' and m∠B = m∠B'
Since, sides of ΔA'B'C' = of the sides of ΔABC
Area of ΔA'B'C' =
Area of ΔABC > Area of ΔA'B'C'
Since, angles of ΔABC and ΔA'B'C' are congruent, both the triangles will be similar.
ΔABC ~ ΔA'B'C'
Therefore, Option (3) and Option (6) are the correct options.
Refer to the diagram shown below.
The given constraints are
(a) y ≥ 24 ft
(b ) x ≤ 10 ft
(c) y ≥ 3x
(d) y ≤ 33 ft
The acceptable region is shown shaded.
A (0, 33) satisfies all conditions
B (4, 36) fails condition (d)
C (4.8, 30.5) satisfies all conditions
D (9, 26) fails condition (c)
E (2, 22) fails condition (a)
Answer:
The acceptable points are A and C.
The given constraints are
(a) y ≥ 24 ft
(b ) x ≤ 10 ft
(c) y ≥ 3x
(d) y ≤ 33 ft
The acceptable region is shown shaded.
A (0, 33) satisfies all conditions
B (4, 36) fails condition (d)
C (4.8, 30.5) satisfies all conditions
D (9, 26) fails condition (c)
E (2, 22) fails condition (a)
Answer:
The acceptable points are A and C.