Question

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.

Answer #1

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

We have a triangle ABC. a=|BC|, b=|CA|, c=|AB| and ∠A=v , ∠B=r ,
and ∠C=z
Calculate c, if we know that ∠C is acute and a=8, b=3 and sin (z) =
1/7

Suppose △ABC and △A'B'C' are triangles such that line AB || to
line A'B', line BC || to line B'C', and line AC || to line A'C'.
Prove that △ABC ~ △A'B'C'.

If in triangle ABC and Triangle XYZ we have AB = XY, AC = XZ,
but m<A > m<X, then BC > YZ. Conversely, if BC > YZ
then m<A > m<X.

Consider the triangle ABC. Suppose that the perpendicular
bisectors of line segments AB and BC intersect at point X. Prove
that X is on the perpendicular bisector of line segment AC.

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.

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

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

Suppose that the incircle of triangle ABC touches AB at Z, BC at
X, and AC at Y . Show that AX, BY , and CZ are concurrent.

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

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