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Period: _________________
GEOMETRY REVIEW SHEET
Polygon:
Poly – Many
Gon - Angles
Triangle:
Tri – 3
Angles
Scalene:
no equal
sides
Isosceles: 2
equal sides
Right Angle: 90°
(perpendicular)
Equilateral:
Equi – equal
Lateral – sides
4 90-degree
angles; 4 equal
sides
Only one pairs of
parallel sides
Regular:
equal sides
Pentagon
Pente – 5
Gon – angles
4 equal sides
Two pairs of
parallel sides
Quadrilateral:
Quad – 4
Lateral – sides
Hexagon
Hex – 6
Gon – angles
Page 1 of 13
PERIMETER AND AREA
Perimeter – the distance around the exterior of a figure
Key: ADD
𝟓+𝟖+𝟔+𝟒=𝟐𝟑 𝒖𝒏𝒊𝒕𝒔
Area – the number of square units needed to fill the space inside a figure
Key: MULTIPLY (or count)
𝟑∗𝟓=𝟏𝟓 𝒖𝒏𝒊𝒕𝒔2
Area Formulas:
Area = 𝟏/𝟐 𝒃𝒉
Area = 𝒃𝒉
Composite (combined) Shapes:
Perimeter – ONLY the exterior (not the inside lines/height)
Area – add the areas of each shape
𝑃 = 6 + 4 + 8 + 6 + 10 + 6
𝑃 = 40 𝑢
1
𝐴 𝑇 = (4 + 10) ∗ 5
2
1
𝐴 𝑇 = (14) ∗ 5 = 35
2
𝐴𝑅 = 10 ∗ 6 = 60
𝑇𝐴 = 35 + 60 = 95𝑢2
Page 2 of 13
Area = 𝟏/(𝒃1+𝒃2)𝒉
TRANSFORMATIONS
Translation: SLIDE a shape while
maintaining size, shape and orientation
Translate the figure 3 units up, 5 units to
the right.
Reflection: FLIP (mirror) a shape across a
line while maintaining the shape and size.
Reflect △ 𝐴𝐵𝐶 across the y-axis.
Rotation: TURN a shape around a fixed
point while maintaining the shape and size.
Rotate △ 𝐴𝐵𝐶 around the origin.
Dilation: EXPAND (or SHRINK) a shape by a
proportional ratio (zoom factor).
Dilate △ 𝐴𝐵𝐶 by a zoom factor of 2.
Page 3 of 13
ANGLE RELATIONSHIPS
Complementary Angles – Two angle measures that add up to 90°.
Supplementary Angles – Two angle measures that add up to 180°.
Vertical Angles – The two opposite (non-adjacent) angles formed by two intersecting lines;
congruent
Markings:

Equal/congruent angles –

Equal/congruent sides –
Page 4 of 13
Parallel Lines and Special Angle Relationships:
Corresponding Angles: Angles which lie in the same position but at different points of
intersection of the transversal. When lines are parallel, they are congruent.
Name the other corresponding
angles in the figure.
Alternate Interior Angles: Angles which lie one on the left and one on the right side of the
transversal, and both are between the pair of lines. When lines are parallel, they are
congruent.
Name the other alternate interior
angles in the figure.
Same-side Interior Angles: Angles which lie on the same side of the transversal and both are
between the pair of lines. When lines are parallel, they are supplementary (= 180°)
Name the other same-side interior
angles in the figure.
Page 5 of 13
TRIANGLE INEQUALITY THEOREM
Not all sets of 3 segments can form a triangle! There are limitations…
 Any side must be less than the sum of the other two sides
 Any side must be greater than the difference of the other two sides
Which of the following sets of 3 lengths cannot form a triangle?
4, 5, 6
3, 3, 3
2, 3, 5
7, 7, 15
8, 9, 16
12, 13, 25
___________________________________________________________________
PYTHAGOREAN THEOREM

Definition – In a right triangle, the sum of the squares of the legs is equal to the square
of the hypotenuse.
 Legs – form the right angle
 Hypotenuse – longest side
(opposite the right angle)
Solve for the missing side in the triangle:
𝒂𝟐 + 𝒃𝟐 = 𝒄𝟐
𝟔𝟐 + 𝒃𝟐 = 𝟏𝟐𝟐
𝟑𝟔 + 𝒃𝟐 = 𝟏𝟒𝟒
𝒃𝟐 = 𝟏𝟎𝟖
𝒃 = √𝟏𝟎𝟖
𝒃 = √𝟑𝟔 ∗ 𝟑 𝒃 = 𝟔√𝟑
Page 6 of 13
SIMILARITY
Definition – two (or more) figures that have the same shape but a different size.
Ratio of Similarity – the ratio between any pair of corresponding sides in similar figures (zoom
factor).
𝑎:𝑏 or 𝑎/𝑏 or “𝑎 to 𝑏”
Finding corresponding parts: Examine any lettering on the figures – the order will tell you
Shapes within shapes:
Key: Big to big; small to small
Page 7 of 13
DETERMINING TRIANGLE SIMILARITY
Similarity means…
Corresponding angles have equal measure
Corresponding sides are proportional
Three conjectures to prove similarity:
 SSS Similarity (SSS ∼):
All three corresponding side lengths share a common ratio.
 AA Similarity (AA ∼):
Two pairs of corresponding angles have equal measures.
 SAS Similarity (SAS ∼):
Two pairs of corresponding sides share a common ratio AND the corresponding angles
between those sides have equal measure.
Page 8 of 13
Are the triangles below similar? If yes, state the conjecture and state the similarity:
DETERMINING TRIANGLE CONGRUENCY
Congruency means… Two figures have the same shape AND the same size.
In other words, the shapes are similar and the side lengths have a common ratio of 1.
Five conjectures to prove congruency…
 SSS (Side-Side-Side) ≅:
If all three pairs of corresponding sides have equal lengths, then the triangles are
congruent.
Page 9 of 13
More congruency conjectures…
 SAS (Side-Angle-Side) ≅:
If two pairs of corresponding sides have equal lengths AND the angles between them
(the included angle) are equal, then the triangles are congruent.
 ASA (Angle-Side-Angle) ≅:
If two angles and the side between them in a triangle are congruent to the
corresponding angles and side in another triangle, then the triangles are congruent.
 AAS (Angle-Angle-Side) ≅:
If two pairs of corresponding angles AND a pair of corresponding sides that are not
between them have equal measures, then the triangles are congruent.
 HL (Hypotenuse-Leg) ≅:
If the hypotenuse and a leg of one right triangle have the same lengths as the
hypotenuse and a leg of another right triangle, then the triangles are congruent.
Page 10 of 13
TRIGONOMETRIC RATIOS
In any right triangle… The sides are proportional to each other in conjunction with the other
acute angles. These ratios are defined in three ways…
Three trigonometric ratios…
 Sine (sin) function
 The ratio of the opposite side from an angle to the hypotenuse
Designated by:
𝐬𝐢𝐧 𝜽 =

𝒐𝒑𝒑𝒐𝒔𝒊𝒕𝒆
𝒉𝒚𝒑𝒐𝒕𝒆𝒏𝒖𝒔𝒆
Cosine (cos) function
 The ratio of the adjacent side from an angle to the hypotenuse
Designated by:
𝐜𝐨𝐬 𝜽 =

𝒂𝒅𝒋𝒂𝒄𝒆𝒏𝒕
𝒉𝒚𝒑𝒐𝒕𝒆𝒏𝒖𝒔𝒆
Tangent (tan) function
 The ratio of the opposite side from an angle to the adjacent side of that same
angle
Designated by:
𝐭𝐚𝐧 𝜽 =
𝒐𝒑𝒑𝒐𝒔𝒊𝒕𝒆
𝒂𝒅𝒋𝒂𝒄𝒆𝒏𝒕
Page 11 of 13
Use SOHCAHTOA as a mnemonic to remember…
sin 𝜃 = 4/5
cos 𝜃 = 3/5
tan 𝜃 = 4/3
To find missing sides of right triangles with an angle and a single given side…
𝟒
𝒉
𝟒
. 𝟗𝟎𝟔𝟑 =
𝒉
. 𝟗𝟎𝟔𝟑𝒉 = 𝟒
𝟒
𝒉=
≈ 𝟒. 𝟒𝟏
. 𝟗𝟎𝟔𝟑
sin 𝟔𝟓° =
To find an angle given the sides of a triangle…
𝟒
𝟓
sin 𝜃 = 𝟎. 𝟖
𝜽 = sin−𝟏 𝟎. 𝟖
𝜽 ≈ 𝟓𝟑. 𝟏𝟑°
sin 𝜽 =
Page 12 of 13
SPECIAL RIGHT TRIANGLES
Two special conditions exist to quickly find the sides of right triangles…

𝟑𝟎°/𝟔𝟎°/𝟗𝟎° Triangle
The ratio of the sides is
𝒙: 𝒙√𝟑: 𝟐𝒙
If 𝑥 = 4, the hypotenuse
is 8, and the other leg
is 4√3.

𝟒𝟓°/𝟒𝟓°/𝟗𝟎° Triangle
The ratio of the sides is
𝒙: 𝒙: 𝒙√𝟐
If the hypotenuse
is 6√2, both of the legs
are 6.
Page 13 of 13