given: angle KLM and angle NML are right angles. angle 2 is congruent to angle 3. Prove: angle 1 is congruent to angle 4

1 answer:

3 0

Angle KLM=angleNML=90°
the sum of angles in a triangle is 180°
since: angle2=angle3=x
angle1=angle4=y because
180°-90°-x=180°-90°-x

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$d^3 a^3 + e^3 a^3 + f^3 a^3 + 3 d e^2 a^3 + 3 d f^2 a^3 + 3 e f^2 a^3 + 3 d^2 e a^3 + 3 d^2 f a^3 + 3 e^2 f a^3 + 6 d e f a^3 \\+ 3 b d^3 a^2 + 3 c d^3 a^2 \\+ 3 b e^3 a^2 + 3 c e^3 a^2 + 3 b f^3 a^2 \\+ 3 c f^3 a^2 + 9 b d e^2 a^2 + 9 c d e^2 a^2 + 9 b d f^2 a^2 + 9 c d f^2 a^2\\ + 9 b e f^2 a^2 + 9 c e f^2 a^2 + 9 b d^2 e a^2 + 9 c d^2 e a^2 + 9 b d^2 f a^2 + 9 c d^2 f a^2 \\+ 9 b e^2 f a^2 + 9 c e^2 f a^2 + 18 b d e f a^2$

$+ 18 c d e f a^2 + 3 b^2 d^3 a + 3 c^2 d^3 a \\+ 6 b c d^3 a + 3 b^2 e^3 a + 3 c^2 e^3 a + 6 b c e^3 a + 3 b^2 f^3 a \\+ 3 c^2 f^3 a + 6 b c f^3 a + 9 b^2 d e^2 a \\+ 9 c^2 d e^2 a + 18 b c d e^2 a + 9 b^2 d f^2 a\\ + 9 c^2 d f^2 a + 18 b c d f^2 a + 9 b^2 e f^2 a + 9 c^2 e f^2 a + 18 b c e f^2 a + 9 b^2 d^2 e a \\+ 9 c^2 d^2 e a + 18 b c d^2 e a + 9 b^2 d^2 f a + 9 c^2 d^2 f a + 18 b c d^2 f a \\+ 9 b^2 e^2 f a + 9 c^2 e^2 f a + 18 b c e^2 f a$

$+ 18 b^2 d e f a + 18 c^2 d e f a + 36 b c d e f a \\+ b^3 d^3 + c^3 d^3 + 3 b c^2 d^3 + 3 b^2 c d^3 + b^3 e^3 + c^3 e^3 \\+ 3 b c^2 e^3 + 3 b^2 c e^3 + b^3 f^3 + c^3 f^3 + 3 b c^2 f^3 + 3 b^2 c f^3 + 3 b^3 d e^2 \\+ 3 c^3 d e^2 + 9 b c^2 d e^2 + 9 b^2 c d e^2 + 3 b^3 d f^2 + 3 c^3 d f^2 + 9 b c^2 d f^2 \\+ 9 b^2 c d f^2 + 3 b^3 e f^2 + 3 c^3 e f^2$

$+ 9 b c^2 e f^2 + 9 b^2 c e f^2 + 3 b^3 d^2 e \\+ 3 c^3 d^2 e + 9 b c^2 d^2 e + 9 b^2 c d^2 e + 3 b^3 d^2 f + 3 c^3 d^2 f \\+ 9 b c^2 d^2 f + 9 b^2 c d^2 f + 3 b^3 e^2 f + 3 c^3 e^2 f + 9 b c^2 e^2 f \\+ 9 b^2 c e^2 f + 6 b^3 d e f + 6 c^3 d e f + 18 b c^2 d e f + 18 b^2 c d e f$