Preparing for the Regents Examination Geometry, AK

5-3 Isosceles and
Equilateral Triangles
(page 74)
1 Statements Reasons
1. Construct a
median from the
vertex formed
by the two congruent
sides of
the triangle, to
form RST with
median −−−
RU .
1. A median of a
triangle is a line
segment with one
endpoint at any
vertex of the
triangle, extending
to the
midpoint of the
opposite side.
2. −−
RS −−
RT 2. Definition of an
isosceles triangle.
3. −−
SU −−
TU 3. Definition of a
median.
4. −−−
RU −−−
RU 4. Reflexive
property of
congruence.
5. RSU RTU 5. SSS SSS.
6. RSU RTU 6. Corresponding
parts of congruent
triangles are
congruent.
2 Statements Reasons
1. Construct a
median from the
vertex formed
by the two congruent
sides of
the triangle, to
form RST with
median −−−
RU .
1. A median of a
triangle is a line
segment with one
endpoint at any
vertex of the triangle,
extending
to the midpoint of
the opposite side.
2. −−
RS −−
RT 2. Definition of an
isosceles triangle.
3. −−
SU −−
TU 3. Definition of a
median.
4. −−−
RU −−−
RU 4. Reflexive property
of congruence.
5. RSU RTU 5. SSS SSS.
20 Chapter 5: Congruence Based on Triangles
6. SRU TRU 6. Corresponding
parts of congruent
triangles are
congruent.
7. −−−
RU bisects SRT. 7. Definition of
angle bisector.
3 Statements Reasons
1. Construct a
median from the
vertex formed
by the two congruent
sides of
the triangle, to
form RST with
median −−−
RU .
1. A median of a
triangle is a line
segment with one
endpoint at any
vertex of the
triangle, extending
to the
midpoint of the
opposite side.
2. −−
RS −−
RT 2. Definition of an
isosceles triangle.
3. −−
SU −−
TU 3. Definition of a
median.
4. −−−
RU −−−
RU 4. Reflexive property
of congruence.
5. RSU RTU 5. SSS SSS.
6. SUR TUR 6. Corresponding
parts of congruent
triangles are
congruent.
7. SUR is a right
angle; TUR is a
right angle.
7. Adjacent congruent
angles are
supplementary.
8. −−−
RU −−
ST 8. Definition of perpendicular
lines.
4 Statements Reasons
1. Construct a
median from the
vertex formed
by the two congruent
sides of
the triangle, to
form ABC with
median −−−
AX .
1. A median of a
triangle is a line
segment with
one endpoint at
any vertex of
the triangle,
extending to the
midpoint of the
opposite side.
2. −−
AB −−
AC 2. Definition of
an equilateral
triangle.