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Chapter 4 – Congruent Triangles
Objectives/Goals
4-1 – Congruent Figures
Be able to define and recognize congruent polygons
Be able to use the corresponding parts of congruent polygons
4-2 – Some Ways to Prove Triangles Congruent
Be able to prove triangles congruent with three postulates
4-3 – Using Congruent Triangles
Be able to give justification for triangles to be congruent
4-4 – The Isosceles Triangle Theorems
Be able to apply the properties of isosceles triangles and know when to use them
4-5 – More Methods of Proving Triangles Congruent
Be able to state and use other ways of proving triangles congruent including HL
and AAS
4-6 – Using More than One Pair of Congruent Triangles
Be able to use one pair of congruent triangles to get another pair
Essential Questions
1.) How do we determine congruent figures?
2.) When can corresponding parts of congruent figures be used?
3.) What are the ways to prove triangles congruent?
4.) What are the properties of perpendicular bisectors?
5.) For isosceles triangles, how do the leg lengths relate to the base angles?
6.) What are the properties of angle bisectors?
Chapter 4 terms to know
Congruent figures
Corresponding parts
CPCTC
Opposite sides
Opposite angles
Included sides
Included angles
Perpendicular planes
Legs of isosceles triangle
Base
Base angles
Vertex angle
Hypotenuse
Legs of a right triangle
Key steps for a proof
Paragraph proof
CHAPTER 4
Postulate 12 SSS – If three sides of one triangle are congruent to three sides of another
triangle, then the triangles are congruent.
Postulate 13 SAS – If two sides and the included angle of one triangle are congruent to two
sides and the included angle of another triangle, then the triangles are
congruent.
Postulate 14 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 triangles are
congruent.
Theorem 4-1 Isosceles Triangle Theorem (BAITC) – If two sides of a triangle are congruent, then the
angles opposite those sides are congruent.
Corollary 1
Corollary 2
Corollary 3
An equilateral triangle is also equiangular.
An equilateral triangle has three 60 angles.
The bisector of the vertex angle of an isosceles triangle is perpendicular to the
base at its midpoint.
Theorem 4-2 ConBAIT – If two angles of a triangle are congruent, then the sides opposite
those angles are congruent.
Corollary
An equiangular triangle is also equilateral.
Theorem 4-3 AAS – If two angles and a non-included side of one triangle are congruent to
the corresponding parts of another triangle, then the triangles are
congruent.
Theorem 4-4 HL – If the hypotenuse and a leg of one right triangle are congruent to the
corresponding parts of another right triangle, then the triangles are
congruent.
Theorem 4-5 If a point lies on the perpendicular bisector of a segment, then the point is equidistant
from the endpoints of the segment.
Theorem 4-6 If a point is equidistant from the endpoints of a segment, then the point lies on the
perpendicular bisector of the segment.
Theorem 4-7 If a point lies on the bisector of an angle, then the point is equidistant from the sides of
the angle.
Theorem 4-8 If a point is equidistant from the sides of an angle, then the point lies on the bisector of
the angle.