Question

Prove: If two angles of a triangle are not congruent, then the
sides opposite those angles are not congruent.

Answer #1

We do this by contradiction...

Given that two angles of traingle are not congruent...

Let us assume that their opposite two side of a triangle are congruent..

So triangle is issoceles triangles...and in issoceles traingle two angles are congruent...or you can use theoram.

Theoram states that , opposite angle of congruent sides are congruent...

So two angles of triangle are congruent... But it is contradiction to given statement...

So our assumption is wrong..

This shows that these two opposite sides of those angles are not congruent..

Any doubt then comment below..

if three angles in one triangle are congruent to three angles in
another triangle,then the two triangles are congruent.true or
false,if it is false make a counterexample

1. Let the angles of a triangle be α, β, and
γ, with opposite sides of length a, b,
and c, respectively. Use the Law of Cosines and the Law of
Sines to find the remaining parts of the triangle. (Round your
answers to one decimal place.)
α = 105°; b =
3; c = 10
a=
β= ____ °
γ= ____ °
2. Let the angles of a triangle be α,
β, and γ, with opposite sides of length
a, b,...

Let the angles of a triangle be α, β, and
γ, with opposite sides of length a, b,
and c, respectively. Use the Law of Sines to find the
remaining sides. (Round your answers to one decimal place.)
β = 99°; γ =
29°; c = 20

Let the angles of a triangle be α, β, and
γ, with opposite sides of length a, b,
and c, respectively. Use the Law of Cosines to find the
remaining side and one of the other angles. (Round your answers to
one decimal place.)
α = 46°; b =
12; c = 18

Draw an example of two non-congruent triangles that
have congruent corresponding angles and two pairs of sides (not
corresponding) congruent. If not, explain why.

show that if the summit and the base angles of two saccheri
quadrilaterals are congruent then the reamining sides are
congruent.

Let 4ABC be an isosceles triangle, where the congruent
sides are
AB and AC. Let M and N denote points on AB and AC
respectively
such that AM ∼= AN. Let H denote the intersection point of MC
with
NB. Prove that the triangle 4MNH is isosceles

If the parts of two triangles are matched so that two angles of
one triangle are congruent to the corresponding angles of the
other, and so that a side of one triangle is congruent to the
corresponding side of the other, then the triangles must be
congruent. Justify this angleangle-corresponding side (AAS)
criterion for congruence. Would AAS be a valid test for congruence
if the word corresponding were left out of the definition?
Explain.

1.
Prove that the difference of the lengths of two sides of a triangle
is less than the third side.
2. Prove that in a triangle one side’s median is less than
half the sum of the other two sides.
3. Prove that the sum of the lengths of a quadrilateral’s
diagonals is less than its perimeter.

Write a proof to show that opposite sides of a parallelogram are
congruent. Be sure to create and name the appropriate geometric
figures. This figure does not need to be submitted.

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 10 minutes ago

asked 10 minutes ago

asked 10 minutes ago

asked 12 minutes ago

asked 14 minutes ago

asked 18 minutes ago

asked 25 minutes ago

asked 27 minutes ago

asked 27 minutes ago

asked 39 minutes ago

asked 39 minutes ago

asked 39 minutes ago