Algebra 1 / Geometry
Unit 8: Triangles and Quadrilaterals
Enduring understandings
By the end of this unit, you will understand that:
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Congruence is a geometrical relationship that can be proved in a variety of ways
Triangle constructions create a variety of constant relationships
Quadrilaterals have a variety of commonalities and differences
Essential questions
By the end of this unit, you will be able to answer these questions:
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How can you prove geometric congruence in triangles?
What unique features of triangle constructions create constant relationships?
How do we distinguish between different quadrilaterals?
Unit Goals
Knowledge
By the end of this unit, you should know:
 Triangle vocabulary: isosceles, equilateral, equiangular (corollaries), midsegments,
bisectors
 Parts of triangles: hypotenuse, legs, base, median, altitude, points of concurrency
(circumcenter, incenter, centroid, orthocenter), base & base angles of isosceles
triangles, (Euler line: extension?), relative measures of opposite angles & sides
 Theorems: third angle of triangle theorem, acute angles of right triangle, congruent
triangles (SSS, SAS, ASA, AAS, HL), congruent polygons, Corresponding Parts of
Congruent Triangles are Congruent (CPCTC), (converse of) Isosceles Triangle, bisector
of the vertex angle of an isosceles triangle
 Properties of quadrilaterals
 Proofs and theorems: opposite sides and angles of parallelogram, diagonals bisect each
other, diagonals of a rectangle are congruent, diagonals of a rhombus are perpendicular
and angle bisectors, base angles and diagonals of isosceles trapezoid, median of
trapezoid
Skills
By the end of this unit, you should be able to:
 Prove of theorems and use the theorems to perform proofs of other geometric
relationships
 Prove triangles, angles or sides congruent with the following five theorems (SSS, SAS,
ASA, AAS, HL) and CPCTC (Corresponding Parts of Congruent Triangles are
Congruent), using flow-chart and two-column proofs
 Recognize the difference between parallelograms, rhombi, trapezoid, rectangles,
squares, kites.
 Define various quadrilaterals.
 Use properties of quadrilaterals.
 Calculate angles and sides of quadrilaterals using algebraic expressions.
 Reinforce solving equations.
 Use informal proof to justify results.
 Investigate different properties of quadrilaterals using Geometer’s Sketchpad.
Triangles and Quadrilaterals
Lesson by lesson
Lesson
Concept
Exercises
Wed 30 Mar
Triangle congruence:
SSS and SAS,
ASA and AAS
p223 Q 32 – 42
p231-2 Q 11 – 31
p238-40 Q 8 - 29
Fri 1 April
Using corresponding parts of congruent triangles
p 246-7 5 – 19
Mon 4
Isosceles, equilateral and right triangles
p254 Q 6 – 20
p262-3 Q 8 – 25
Wed 6
Overlapping triangles
Constructions in triangles: midsegments and
bisectors
p 268-70 Q8 – 26
p288-90 Q7 – 41
p296-7 Q 6 – 22
p 305 Q 14 – 18
Fri 8
Constructions in triangles: midsegments and
altitudes medians
Triangle Inequality Theorem
p 312-3 Q 8 – 27
p 329 Q 9 – 32
Mon 11
GSP Investigation: constructions
Quadrilaterals: parallelograms
Worksheet
pp 364-5 Q9 – 30
pp 372-3 Q 7 – 25
Wed 13
Rhombus, rectangle, square.
Trapezoid and kite
pp 379-80 Q 9 – 44
pp386-7 Q 8 – 19
pp 394-6 Q 7 – 52
Fri 15
Quiz
Mon 18
Review
Wed 20
Test
Fri 22
Connections: parallel lines and triangles
Review worksheet
Worksheet