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UNIT 8
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Activating Prior Knowledge
Classifying Triangles
Quick Review
Here are two ways to classify triangles.
• By side length
An equilateral triangle
has all sides equal.
An isosceles triangle
has 2 equal sides.
A scalene triangle
has all sides different.
A right triangle
has one 90° angle.
An obtuse triangle
has one angle greater
than 90°.
• By angle measure
An acute triangle
has all angles less
than 90°.
Check
Use square dot paper or triangular dot paper.
1. Draw an isosceles triangle.
Is it acute, obtuse, or right? How do you know?
2. Draw an obtuse triangle.
Is it equilateral, scalene, or isosceles? How do you know?
3. Can you draw an obtuse isosceles triangle?
If you can, draw it.
If you cannot draw the triangle, say why it cannot be drawn.
4. Can you draw a right equilateral triangle?
If you can, draw it.
If you cannot draw the triangle, say why it cannot be drawn.
Activating Prior Knowledge: Unit 8
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Properties of a Rhombus
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Quick Review
A rhombus is a parallelogram with all sides equal.
The properties of a rhombus are:
• Opposite angles are equal.
• The diagonals intersect at right angles.
• Opposite sides are parallel.
• The diagonals bisect each other.
• Diagonals bisect the angles.
Example
Look at rhombus PQRS.
a) Name all pairs of parallel sides.
b) What is the measure of ∠PCQ? How do you know?
c) What do you know about the measures of ∠QRC
and ∠SRC?
d) What do you know about the lengths of SC and CQ?
Solution
a) Opposite sides are parallel.
So, RQ is parallel to SP and SR is parallel to PQ.
b) The diagonals of a rhombus intersect at right angles.
So, ∠PCQ = 90°
c) The diagonals of a rhombus bisect the angles.
So, ∠QRC = ∠SRC
d) RP is the perpendicular bisector of SQ.
So, SC = CQ
Check
5. Use a ruler and a protractor.
Draw any rhombus ABCD.
Draw the diagonals of the rhombus.
a) Name:
i) all equal sides
ii) pairs of parallel sides
iii) all equal angles
iv) all right angles
v) the perpendicular bisector of AC vi) the perpendicular bisector of BD
b) Name pairs of equal line segments created by the diagonals.
Activating Prior Knowledge: Unit 8
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Sample Answers: Activating Prior Knowledge
Unit 8
Classifying Triangles
1. Answers will vary depending on triangle drawn.
Acute isosceles: all angles less than 90°, and 2 equal angles
Obtuse isosceles: one angle greater than 90°, other two angles equal
Right isosceles: one 90° angle and two 45° angles
2. Answers will vary depending on triangle drawn.
Obtuse equilateral: cannot be drawn; an equilateral triangle always has
three equal angles of 60°.
An obtuse angle is greater than 90°.
Obtuse scalene: one angle greater than 90°, and all sides different
Obtuse isosceles: one angle greater than 90°, other two angles equal
3. Yes, for example: Each equal angle measures 33° and the obtuse angle measures 114°.
Each equal side measures 1.7 cm. The third side measures 2.9 cm.
4. No, an equilateral triangle always has three equal angles of 60°.
A right triangle has one angle of 90°.
Properties of a Rhombus
5. Answers may vary. For example
a)
i) AB = BC = CD = DA
ii) AD is parallel to BC; AB is parallel to CD
iii) ∠A = ∠C; ∠D = ∠B; ∠DAE = ∠BAE = ∠BCE = ∠DCE; ∠ADE = ∠CDE = ∠ABE = ∠CBE;
∠AED = ∠AEB = ∠DEC = ∠BEC
iv) ∠AED, ∠AEB, ∠DEC, ∠BEC
v) DB
vi) AC
b) DE = EB and AE = EC
Activating Prior Knowledge: Unit 8
The right to reproduce this page is restricted to purchasing schools.
This page may have been modified from its original. Copyright © 2009 Pearson Education Canada