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Studying Guide
Carmeno and Ariana
Table of Contents
• 4.1: Classifying Triangles • 4.5:Proving Congruence
• 4.2:Angles of Triangles
• 4.6: Isosceles Triangles
• 4.3: Congruent Triangles • 5.1: Bisector, Medians,
and Altitudes
• 4.4:Proving Congruence • Conclusion
4.5: Proving Congruence
G
H
Line GK is congruent to line HJ.
Line GH is congruent to line JK.
K
J
X
W
SAS (Side . Angle . Side): Two sides and
the included angle of one triangle are
congruent to two sides and the
included angles of the other triangle.
Y
Z
SAS (Side . Angle . Side): Two sides and
the included angle of one triangle are
congruent to two sides and the
included angles of the other triangle.
Line WX is congruent to line YZ.
Angle X is congruent to angle Z.
Line WZ is most likely congruent to line
XY.
4.6: Bisectors, Medians, and Altitudes
G
6x - 5
X
5x
J
H
60°
3x + 8
Z
Y
4x - 4
6x – 5 = 5x
-6x
-6x
-5 = -1x
-1 -1
5=X
3x + 8 = 4x – 4
+4
+4
3x + 12 = 4x
- 3x
-3x
12 = X
5.1 Bisectors, Medians, and Altitudes
Find x if line AD is an altitude of
triangle ABC.
2x – 15 = x + 7
What I did was I added 15 to both
sides that way I’m left with 2x on
one side and x + 22 on the other
side. I then subtracted the x from
x+22, and my final product was x =
22. I then plugged 22 into the
equation for line AD and got 82°.
Find x if line PS is median of triangle
PQR.
10x – 7 = 5x + 3
What I did was add 7 to both sides that
way I am left with the equation 10x =
5x + 10. I then subtracted 5x from the
right side of the equal sign and I ended
up with 5x = 10. I then had to divide by
5; I was left with x = 2. I plugged 2 into
the x value of the equation 15x + 42.
When you simplify the equation you
should then have: 30 + 42; 72° is the
final answer.
Conclusion
Three main messages to take from this chapter.
• A few things that are important about this chapter might
be learning what Isosceles, scalene, and equilateral
triangles are, and how they differ from each other. Also,
finding how a triangle is congruent and what sides and
angles are congruent might be an important part about
this chapter. Methods to find out how a triangle is
congruent is also very helpful in this study guide. All
corresponding parts of one triangle are congruent to the
corresponding parts of the other triangle; as long as you
know this then you would know how to tell whether a
triangle is congruent or not. This chapter is full of
helpful information to help identify triangles and their
angles.