Download 11.1

Chapter 11: Additional Topics of Geometry
Section 11.1: Congruence and Triangles
Congruent Polygons
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Congruent Polygons: Two polygons are congruent if and only if there is a correspondence between
their vertices such that all of their corresponding sides and corresponding interior angles are of equal
measure.
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Constructions: Congruent line segment
Congruent Triangles
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Congruent Triangles: Two triangles ΔABC and ΔDEF are congruent if and only if the vertices A, B, C
and D, E, F can be paired so that corresponding angles and corresponding sides are congruent. If A is
paired with D, B with E, and C with F, then
≅
,
≅
,
≅
, ∠ABC ≅ ∠DEF, ∠BCA ≅
∠EFD, and ∠CAB ≅ ∠FDE.
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Side, Angle, Side (SAS): If two sides and the included angle (the angle formed by the rays containing
the two sides) of one triangle are congruent to two sides and the included angle of a second triangle, then
the two triangles are congruent.
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Side, Side, Side (SSS): If three sides of one triangle are congruent to three sides of a second triangle,
then the two triangles are congruent.
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Angle, Side, Angle (ASA): If two angles and the included side of one triangle are congruent to two
angles and the included side of another triangle, then the two triangles are congruent.
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Angle, Angle, Side (AAS): If two angles and a corresponding side of one triangle are congruent to two
angles and a corresponding side of a second triangle, then the two triangles are congruent.
Common Error
• See figure 11-10 page 534
Characteristics of Right Triangles
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Hypotenuse: Longest side located opposite the right angle
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Legs: Two segments contained within the rays forming the right angle
Equilateral and Isosceles Triangles
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Properties of Equilateral and Isosceles Triangles:
o If a triangle is isosceles, the angles opposite the congruent sides are congruent
o If two angles of a triangle are congruent, the triangle is an isosceles triangle, where the sides
opposite congruent angles are congruent
o If a triangle is equilateral, all three angles are congruent
o If three angles of a triangle are congruent, the triangle is an equilateral triangle
The Pythagorean Theorem and Its Converse
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Converse of the Pythagorean Theorem: If the square of the measure of one side of a triangle is equal
to the sum of the squares of the measures of the other two sides, the triangle is a right triangle
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Pythagorean Theorem: The sum of the squares of the legs is equal to the square of the hypotenuse: a2
+ b2 = c2
Proof of the Pythagorean Theorem
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Which former US President did an independent proof of the Pythagorean Theorem?
Exercise Sets:
Homework:
p. 538: 1acef, 2ace, 4ac, 5, 9, 10ac, 11, 12