Spring Semester Exam Material
7.1/7.2/7.3 Proportions and Similar Polygons – Match similar figures to find missing parts.
7.4 Parallel Lines and Proportional Parts – Parallel lines divide segments proportionally.
7.5 Parts of Similar Triangles – if 2 triangles are similar then their medians are proportional, too.
8.1 Geometric Mean – This works for a triangle with an altitude drawn to hypotenuse.
8.2 Pythagorean Theorem and Its Converse – a^2 + b^2 = c^2
8.3 Special Right Triangles – 45/45/90 and 30/60/90
8.4/8.5 Trigonometric Ratios – SOHCAHTOA
8.6 Law of Sines – This applies when you have 2 angles and 2 side lengths of triangle, but 1 is a mystery.
8.7 Law of Cosines – This applies when you have 1 angle and 3 side lengths of triangle, but 1 is a mystery.
9.1/9.2/9.3 Reflections and Translations and Rotations
9.5 Dilations – figure either shrinks (scale factor less than 1) or grows (greater than 1)
9.6 Vectors – find magnitude (length) and direction (angle between 00 and 3600)
10.1 Circles and Circumference – C = 2πr (arc length is some fraction of circumference)
10.2 Measuring Angles and Arcs – central angles add to 360 (so do their arcs)
10.3 Arcs and Chords – congruent chords are same distance from center
10.4 Inscribed Angles – measures half of inscribed arc
10.5 Tangents – perpendicular to radius, 2 tangent segments from same exterior point are congruent
10.6 Secants/Tangents/Angles – angle in = ½ sum of arcs angle on = ½ arc angle outside = ½ diff
10.7 Special Segments in a Circle – parts = parts OR out·whole = out·whole
11.1 Area of Parallelograms – A = b·h (might need to use SOHCAHTOA)
11.2 Area of Triangles/Trapezoids/Rhombi – A = ½ b·h A = ½ (b1 + b2) ·h A = ½ d1·d2
11.3 Area of Regular Polygons/Circles – polygon – find area of 1 triangle then multiply by # of them
circle – A = πr2
11.4 Area of Composite Figures – find the area of the shapes that make the figure
11.5 Area of Sectors – some fraction of circle area (based on central angle or arc measure out of 360)
12.1 Representations of 3D Figures – dot paper, orthographic drawing
12.2/12.3 Surface Area of Prisms – add all lateral faces and 2 bases
12.3 Surface Area of Cylinders – add sides of cylinder (2πr·h) to circle bases (2·πr2)
12.4 Surface Area of Pyramids – add lateral faces (will need slant height) to base area
12.5 Surface Area of Cones – add lateral area (π·r·l) to circle base (πr2)
12.6 Surface Area of Spheres – 4·πr2
13.1 Volume of Prisms and Cylinders – base area · height
13.2 Volume of Pyramids and Cones – (1/3)·(base area · height)
13.3 Volume of Spheres – (4/3)·πr3
13.4 Comparing Similar Solids – find side ratio (scale factor), square for area ratio, cube for volume ratio
13.5 Graphing in 3D – use dot paper
Counting Principles – OR = addition, AND = multiplication
Probability – # of ways to get result you want divided by # of possible results
For extra help refer to postings on Canvas or go to glassgeometry.weebly.com.
You can use a note sheet on the semester exam --- one side of an 8.5 x 11 inch piece of paper.
7.1/7.2/7.3 Proportions and Similar Polygons – Match similar figures to find missing parts.
7.4 Parallel Lines and Proportional Parts – Parallel lines divide segments proportionally.
7.5 Parts of Similar Triangles – if 2 triangles are similar then their medians are proportional, too.
8.1 Geometric Mean – This works for a triangle with an altitude drawn to hypotenuse.
8.2 Pythagorean Theorem and Its Converse – a^2 + b^2 = c^2
8.3 Special Right Triangles – 45/45/90 and 30/60/90
8.4/8.5 Trigonometric Ratios – SOHCAHTOA
8.6 Law of Sines – This applies when you have 2 angles and 2 side lengths of triangle, but 1 is a mystery.
8.7 Law of Cosines – This applies when you have 1 angle and 3 side lengths of triangle, but 1 is a mystery.
9.1/9.2/9.3 Reflections and Translations and Rotations
9.5 Dilations – figure either shrinks (scale factor less than 1) or grows (greater than 1)
9.6 Vectors – find magnitude (length) and direction (angle between 00 and 3600)
10.1 Circles and Circumference – C = 2πr (arc length is some fraction of circumference)
10.2 Measuring Angles and Arcs – central angles add to 360 (so do their arcs)
10.3 Arcs and Chords – congruent chords are same distance from center
10.4 Inscribed Angles – measures half of inscribed arc
10.5 Tangents – perpendicular to radius, 2 tangent segments from same exterior point are congruent
10.6 Secants/Tangents/Angles – angle in = ½ sum of arcs angle on = ½ arc angle outside = ½ diff
10.7 Special Segments in a Circle – parts = parts OR out·whole = out·whole
11.1 Area of Parallelograms – A = b·h (might need to use SOHCAHTOA)
11.2 Area of Triangles/Trapezoids/Rhombi – A = ½ b·h A = ½ (b1 + b2) ·h A = ½ d1·d2
11.3 Area of Regular Polygons/Circles – polygon – find area of 1 triangle then multiply by # of them
circle – A = πr2
11.4 Area of Composite Figures – find the area of the shapes that make the figure
11.5 Area of Sectors – some fraction of circle area (based on central angle or arc measure out of 360)
12.1 Representations of 3D Figures – dot paper, orthographic drawing
12.2/12.3 Surface Area of Prisms – add all lateral faces and 2 bases
12.3 Surface Area of Cylinders – add sides of cylinder (2πr·h) to circle bases (2·πr2)
12.4 Surface Area of Pyramids – add lateral faces (will need slant height) to base area
12.5 Surface Area of Cones – add lateral area (π·r·l) to circle base (πr2)
12.6 Surface Area of Spheres – 4·πr2
13.1 Volume of Prisms and Cylinders – base area · height
13.2 Volume of Pyramids and Cones – (1/3)·(base area · height)
13.3 Volume of Spheres – (4/3)·πr3
13.4 Comparing Similar Solids – find side ratio (scale factor), square for area ratio, cube for volume ratio
13.5 Graphing in 3D – use dot paper
Counting Principles – OR = addition, AND = multiplication
Probability – # of ways to get result you want divided by # of possible results
For extra help refer to postings on Canvas or go to glassgeometry.weebly.com.
You can use a note sheet on the semester exam --- one side of an 8.5 x 11 inch piece of paper.