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UNIT 4: GEOMETRY, ANGLES, AND
SIMILAR TRIANGLES
Final Exam Review
TOPICS TO INCLUDE
Vocabulary
Angle Pair Relationships
Triangle Sum Theorem
Similar Triangles
Midsegment of a Triangle
VOCABULARY
Congruent – Exactly the SAME SIZE
Midpoint – The MIDDLE POINT of a segment
Bisector – Cuts a segment or angle in HALF
Parallel – 2 lines that never TOUCH
Perpendicular – 2 lines that intersect at a 90° ANGLE
Transversal – a line that intersects 2 PARALLEL LINES
VOCABULARY
Complementary Angles – 2 or more angles that
add up to 90°
Supplementary Angles – 2 or more angles that add
up to 180°
Linear Pair – 2 angles that are ADJACENT and
add up to 180°
Vertical Angles – 2 angles that are formed by an X.
They are the angles that are OPPOSITE from each
other
ANGLE PAIR RELATIONSHIPS
Corresponding Angles – 2 ANGLES THAT ARE IN THE
SAME POSITION AT DIFFERENT INTERSECTIONS



Corresponding Angles:
1 and 5
3 and 7
2 and 6
4 and 8
ANGLE PAIR RELATIONSHIPS
Alternate Interior Angles – 2 ANGLES THAT ARE
INSIDE THE PARALLEL LINES BUT ON OPPOSITE SIDES
OF THE TRANSVERSAL


Alternate Interior Angles:
3 and 6
4 and 5
ANGLE PAIR RELATIONSHIPS
Alternate Exterior Angles – 2 ANGLES THAT ARE
OUTSIDE THE PARALLEL LINES BUT ON OPPOSITE
SIDES OF THE TRANSVERSAL


Alternate Exterior Angles:
1 and 7
2 and 8
ANGLE PAIR RELATIONSHIPS
Consecutive Interior Angles – 2 ANGLES THAT ARE
INSIDE THE PARALLEL LINES AND ON THE SAME SIDE
OF THE TRANSVERSAL


Consecutive Interior Angles:
3 and 5
4 and 6
ANGLE PAIR RELATIONSHIPS
Use the picture to determine if the angles are Supplementary, Vertical,
Corresponding, Alternate Interior, Alternate Exterior, Consecutive, or No
Relationship






1. Angles 1 and 3
2. Angles 3 and 5
3. Angles 2 and 8
4. Angles 1 and 6
5. Angles 4 and 5
6. Angles 5 and 6
ANGLE PAIR RELATIONSHIPS
If 2 lines are parallel,
Vertical Angles are CONGRUENT
Corresponding Angles are CONGRUENT
Alternate Interior Angles are CONGRUENT
Alternate Exterior Angles are CONGRUENT
Consecutive Angles are SUPPLEMENTARY, which
means, add up the angles and set them equal to 180°
ANGLE PAIR RELATIONSHIPS
Now try these:
1.
2.
TRIANGLE SUM THEOREM
The 3 angles in a triangle always ADD
UP TO 180°
Example
24 + 88 + x = 180
112 + x = 180
x = 68°
TRIANGLE SUM THEOREM
You try:
1.
2.
SIMILAR TRIANGLES
There are 3 ways to prove that triangles are similar
1. ANGLE – ANGLE (AA) – Prove that 2 angles are
CONGRUENT
2. SIDE – ANGLE – SIDE (SAS) – Prove the 2 sides and
PROPORTIONAL and 1 angle is CONGRUENT
3. SIDE – SIDE – SIDE (SSS) – Prove that all 3 sides are
PROPORTIONAL
SIMILAR TRIANGLES
Example
1. The triangles share an ANGLE
at the top of the triangles
2. Set up the proportions
10
5
=
8
4
The proportions are equal!
THE TRIANGLES ARE SIMILAR BY SAS and ∆𝑸𝑹𝑺~∆𝑸𝑻𝑾
SIMILAR TRIANGLES
You Try
1.
2.
Reason: ____________
Reason: _____________
∆𝑫𝑨𝑹~∆______________
∆𝑨𝑩𝑪~∆_______________
MIDSEGMENT OF A TRIANGLE THEOREM
The Midsegment of a Triangle Theorem states that the misdsegment
of a triangle is equal to HALF of the THIRD side
BEFORE setting up an equation, MULTIPLY the midsegment by 2
and then solve.
Example:
2(5X – 1) = 58
10X – 2 = 58
10X = 60
X=6
MIDSEGMENT OF A TRIANGLE THEOREM
Now you try:
ALL DONE