Download Side-Angle-Side is a rule used in geometry to prove triangles

Side-Angle-Side is a rule used in geometry to prove
triangles congruent. The rule states that if two sides and
the included angle are congruent to two sides and the
included angle of a second triangle, the two triangles are
congruent. An included angle is an angle created by two
sides of a triangle.
1. Problem: Is triangle PQR congruent to
triangle STV by SAS? Explain.
Solution: Segment PQ is congruent
to segment ST because
PQ = ST = 4.
Angle Q is congruent to
angle T because
angle Q = angle T = 100 degrees.
Segment QR is congruent
to segment TV because QR = TV = 5.
Triangle PQR is congruent
to triangle STV by Side-Angle-Side.
Side-Side-Side is a rule used in geometry to prove
triangles congruent. The rule states that if three sides of
one triangle are congruent to three sides of a second
triangle, the two triangles are congruent.
1. Problem: Show that triangle QYN is congruent
to triangle QYP.
Solution: Segment QN is congruent to
segment QP and segment YN is
congruent to segment YP because that
information is given in the figure.
Segment YQ is congruent to segment
YQ by the Reflexive Property of Congruence, which says any figure is
congruent to itself.
Triangle QYN is congruent to triangle
QYP by Side-Side-Side.
Angle-Side-Angle is a rule used in geometry to prove
triangles are congruent. The rule states that if two angles
and the included side of one triangle are congruent to two
angles and the included side of another triangle, the
triangles are congruent. An included side is a side that is
common to (between) two angles. For example, in the
figure used in the problem below, segment AB is an
included side to angles A and B.
1.
Problem: Show that triangle BAP is congruent
to triangle CDP.
Solution: Angle A is congruent to angle D
because they are both right angles.
Segment AP is congruent to segment DP
because both have measures of 5.
Angle BPA and angle CPD are congruent
because vertical angles are congruent.
Triangle BAP is congruent to triangle
CDP
by Angle-Side-Angle.
Angle-Angle-Side is a rule used in geometry to prove
triangles are congruent. The rule states that if two angles
and a nonincluded side of one triangle are congruent to
two angles and the corresponding nonincluded side of
another triangle, the two triangles are congruent.
1.
Problem: Show that triangle CAB is congruent
to triangle ZXY.
Solution: Angle A and angle Y are congruent
because that information is given
in the figure.
Angle C is congruent to angle Z
because that information is given
in the figure.
Segment AB corresponds to segment XY and
they are congruent because that
information is given in the figure.
Triangle CAB is congruent to triangle
ZXY
by Angle-Angle-Side.
When two triangles are congruent, all six pairs of
corresponding parts (angles and sides) are congruent.
This statement is usually simplified as corresponding parts
of congruent triangles are congruent, or CPCTC for short.
1.
Problem: Prove segment BC is congruent to
segment CE.
Solution: First, you have to prove that triangle
CAB is congruent to triangle CED.
Angle A is congruent to angle D
because that information is given
in the figure.
Segment AC is congruent to segment CD
because that information is given
in the figure.
Angle BCA is congruent to angle DCE
because vertical angles are
congruent.
Triangle CAB is congruent to triangle
CED
by Angle-Side-Angle.
Now that you know the triangles are
congruent, you know that all
corresponding parts must be congruent.
By CPCTC, segment BC
is congruent to segment CE.