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Chapter 3 Review
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CH4- Triangle Inequalities
Skew lines are noncoplanar lines that are neither parallel nor intersecting. CH4- Triangle Inequalities F G
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Parallel planes are planes that do not intersect
F G C B plane HEFG ???? plane ADBC plane HEDA plane GFBC ???? plane HGBA plane EFCD ????
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CH4- Triangle Inequalities
A transversal is a line that intersects two or more coplanar lines in a different point. t m k NOTE: t is the transversal of line m and k
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<10 and <13 AI <8 and <6 CA <15 and <14 CA
Classify the following angle pairs: 1 2 8 7 9 10 16 15 11 12 13 14 3 4 6 5 <10 and <13 AI <8 and <6 CA <15 and <14 CA <7 and <6 SSI <15 and <11 AI <4 and <16 Not related <10 and <11 SSI
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Postulate If two parallel lines are cut by a transversal, then corresponding angles are congruent. 1 2 8 7 3 4 6 5
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Theorem If two parallel lines are cut by a transversal, then alternate interior angles are congruent. 1 2 8 7 3 4 6 5
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Theorem If two parallel lines are cut by a transversal, then same side interior angles are supplementary. 1 2 8 7 3 4 6 5
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Theorem If a transversal is perpendicular to one of the two parallel lines, then it is perpendicular to the other one also. 1 2 8 7 3 4 6 5
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Theorem In a plane two lines perpendicular to the same line are parallel. t m n
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Theorem Two lines parallel to a third line are parallel to each other.
If and THEN
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TYPES OF TRIANGLES – Classification by sides
Scalene – no sides congruent.
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TYPES OF TRIANGLES – Classification by sides
Isosceles– At least two sides congruent.
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TYPES OF TRIANGLES – Classification by sides
Equilateral – all sides are congruent.
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TYPES OF TRIANGLES – Classification by angles
Acute – three acute angles.
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TYPES OF TRIANGLES – Classification by angles
Obtuse – one obtuse angle.
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TYPES OF TRIANGLES – Classification by angles
Right – one right angle
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TYPES OF TRIANGLES – Classification by angles
Equiangular – all angles are congruent
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THEOREM The sum of the measures of the angles of a triangle is 180
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Corollary If two angles of one triangle are congruent to two angles of another triangle, then the third angles are congruent.
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Corollary Each angle of an equiangular triangle has measure of 60 degrees.
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Corollary In a triangle, there can be at most one right angle or obtuse angle.
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Corollary The acute angles of a right triangle are complementary.
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Exterior Angle Theorem
The measure of an exterior angle of a triangle equals the sum of the measures of the two remote interior angles.
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A regular polygon is both equiangular and equilateral
website
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The sum of the measures of the angles of a convex polygon is
Where n is the number of sides. EXAMPLE: Find the sum of the measures of the angles of a nonagon. (9-2)180 (7)180 1260
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The measure of each interior angle of an equiangular polygon is
Where n is the number of sides Find the measure of each interior angle of a regular octagon.
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The sum of the measures of the exterior angles of a convex polygon (one at each vertex) is 360
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The measure of each exterior angle of an equiangular polygon is
Where n is the number of sides Find the measure of each exterior angle of a regular octagon.
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