Question

Prove that if A*B*C, then ray AB = ray AC and ray BC is a subset of ray AC

Answer #1

Prove that given △ABC and △A′B′C′, if we have AB ≡ A′B′ and
BC≡B′C′,then B<B′ if and only if AC<A′C′. You cannot use
measures.

prove that if C is an element of ray AB and C is not equal to A,
then ray AB = ray AC using any of the following corollarys
3.2.18.) Let, A, B, and C be three points such that B lies on
ray AC. Then A * B * C if and only if AB < AC.
3.2.19.) If A, B, and C are three distinct collinear points,
then exactly one of them lies between the other two.
3.2.20.)...

represent the simplest reduction of
(ab' + ac)'
a) a' + bc'
b) a' + b'c
c) a + bc'
d) a + bc

Prove: P(A ∪ B ∪ C) = P(A) + P(Ac ∩ B) + P(Ac ∩ Bc ∩ C)

given a line AB and a point C not on AB, prove that there is a
Ray AD such that AC is between AB and AD

Prove the following identity on languages A, B, C: A(B ∪
C) = AB ∪ AC
Find a counterexample to the following identity on
languages A, B: A* ∩ B* = (A∩B)*

Which statements could be used to prove that ΔABC and ΔA′B′C′
are congruent?
A. ∠A≅∠A′∠A≅∠A′, ∠B≅∠B′∠B≅∠B′, and ∠C≅∠C′∠C≅∠C′
B. AB⎯⎯⎯⎯⎯⎯⎯≅A′B′⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯AB¯≅A′B′¯,
BC⎯⎯⎯⎯⎯⎯⎯⎯≅B′C′⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯BC¯≅B′C′¯, and ∠A≅∠A′∠A≅∠A′
C. AB⎯⎯⎯⎯⎯⎯⎯≅A′B′⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯AB¯≅A′B′¯, ∠A≅∠A′∠A≅∠A′, and
∠C≅∠C′∠C≅∠C′
D. ∠A≅∠A′∠A≅∠A′, AC⎯⎯⎯⎯⎯⎯⎯⎯≅A′C′⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯AC¯≅A′C′¯, and
BC⎯⎯⎯⎯⎯⎯⎯⎯≅B′C′⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯

Prove
(a). Events A and B are independent if and only if Ac
and Bc are independent.
(b). If events A and B both have a positive probability and are
disjoint, then they cannot be independent.

1. (a) Let a, b and c be positive integers. Prove that gcd(ac,
bc) = c x gcd(a, b). (Note that c gcd(a, b) means c times the
greatest common division of a and b)
(b) What is the greatest common divisor of a − 1 and a + 1?
(There are two different cases you need to consider.)

In △ABC, AB = 15 cm, BC = 10 cm, and AC = 6 cm. Find the measure
of angle B to the nearest degree.

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