Download Honors Geometry - Unit 4 Review Triangle Basics • Triangles are

Honors Geometry - Unit 4 Review
Triangle Basics
 Triangles are classified by angles (acute, obtuse, right, equiangular) as well as by sides (scalene,
isosceles, equilateral)
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
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The interior angles of a triangle = 180
The exterior angle of a triangle = sum of the two remote interior angles of a triangle
Angle-Side relationship: Longest side is opposite the largest angle, shortest side is opposite the

smallest angle, etc.
Triangle Inequality: The sum of the two shortest sides of a triangle must be greater than the
longest side.
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The Median of a triangle is a segment joining the vertex to the midpoint of the opposite side.
The Altitude of a triangle is a perpendicular segment joining the vertex to the opposite side.
Isosceles and Equilateral Triangles
 In an isosceles triangle, 2 sides of a triangle   angles opposite the sides are . These  angles are
known as the “base” angles of an isosceles triangle.
 Equilateral Triangle  Equiangular Triangle
Congruent Triangles

Congruent triangles have 3 sets of corresponding angles that are congruent and 3 sets of
corresponding sides that are congruent.
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Use methods of SSS, SAS, ASA, and AAS to prove triangles are congruent
CPCTC: Use after you prove two triangles are congruent to prove other statements are true.
Constructions
 Use a straight edge and compass to construct the following:
 Copy a segment or an angle
 Bisect a segment or an angle
 Draw a line perpendicular to a segment through a point on the segment
 Draw a line perpendicular to a segment through a point NOT on the segment
 Draw a line parallel to a given line (either by corresponding angles or by perpendicular lines)
 Copy a triangle using SSS, SAS, ASA, or AAS
 Construct a triangle that is twice or half the size of a given triangle.
 Construct an equilateral triangle, a right triangle, or an isosceles triangle with given information.
 Construct the median, altitude, angle bisector or perpendicular bisector of a triangle.
Review Problem Set
1. Classify the following triangles by its angles and sides.
a.
b.
c.
2. Find the missing measures.
a.
3. Solve for x.
a.
b.
c.
b.
c.
4. Order the angles from smallest to largest.
a.
b. In RQP
5. Order the sides from shortest to longest
a.
b. In ABC
QP=15
RP=25
mA=35
mB=73
RQ=13
mC=72
6. Two sides of a triangle have the following measures. Find the range of possible measures for the
third side. Write your answer as an inequality
a. 13, 6
b. 2, 7
c. 5, 5
7. Find the value of x.
a.
b.
c.
d.
e.
f.
8. State if the two triangles are congruent, and if so, by what theorem or postulate
a.
b.
c.
d.
e.
f.