Angle Relationships, Similarity and
Parallelograms
 Point
 Line
 Plane
 Lines
that intersect to form right angles.
What is the symbol for perpendicular?
It looks like “”.
 Review
your worksheets.
 What does a midpoint of a segment do?
 It makes two congruent segments.
 What does a bisector of an angle do?
 It makes two congruent angles.
 It
means objects are the same shape and
size.
 Set them equal.
 Vertical
angles
 Linear Pair
 Complementary angles
 Supplementary angles
 Vertical
 …looks
angles are congruent
like a bow tie
 Linear
pair angles have a sum of 180°
 Complementary
 Supplementary
angles have a sum of 90°.
angles have a sum of 180°.
 If
the lines are parallel, then
alternate interior angles are
congruent. (Look for Z)
 If the lines are parallel, then
corresponding angles are
congruent. (Look for F)
 If the lines are parallel, then
consecutive interior angles are
supplementary. (C – supp)
 Reflexive
⦟CAT≅ ⦟𝐶𝐴𝑇 or AB = AB
 Symmetric
If ⦟CAT≅ ⦟𝐷𝑂𝐺, 𝑡ℎ𝑒𝑛 ⦟DOG≅ ⦟𝐶𝐴𝑇
or If 40 = x + 2, then x + 2 = 40
 Transitive
If ⦟CAT≅ ⦟𝐷𝑂𝐺, 𝑎𝑛𝑑 ⦟DOG≅ ⦟𝑅𝐴𝑇,
then If ⦟CAT≅ ⦟𝑅𝐴𝑇.
Polygons
whose
corresponding side lengths
are proportional and
corresponding angles are
congruent.
Ratio
of the lengths of
two corresponding sides
(always reduce)
If
two polygons are similar
then the ratio of their
perimeters is equal to the
ratios of the corresponding
side lengths.
AA~
SAS~
SSS~
If
two angles of one
triangle are congruent to
two angles of another
triangle, then the
triangles are similar.
 If
an angle of one triangle is
congruent to an angle of another
triangle and the lengths of the sides
including these angles are
proportional, then the triangles are
similar.
If
the lengths of the
corresponding sides of two
triangles are proportional,
then the triangles are
similar.
A
line is parallel to the third side of a
triangle if and only if it divides two sides of
the triangle proportionally.
𝐵𝐷
𝐷𝐴
=
𝐵𝐸
𝐸𝐶
DE ⃒⃒AC
iff
If
two similar solids have a scale
factor of a:b, then the
corresponding areas have a ratio
of a²:b², and corresponding
volumes have a ratio of 𝑎3 : 𝑏 3 .
 One
pyramid has a height of 9 feet and the
other has a height of 12 feet. If the two
pyramids are similar, then
 What is the scale factor of the smaller to the
larger?
 Answer: 3:4
 What is the scale factor of the area of their
bases?
 Answer: 9:16
 The volume of the smaller is 28 meters
cubed. What is the volume of the larger?
 Answer: 66.37 meters cubed
 If
a triangle has two congruent sides, then
the angles opposite those sides are
congruent.
 Or Base angles of an isosceles triangle are
congruent.
It
is a quadrilateral with two
pair of opposite sides
parallel.
Opposite
sides are parallel.
Opposite sides are congruent.
Opposite angles are congruent.
Consecutive angles are
supplementary.
Diagonals bisect each other.
A
quadrilateral with four right angles.
What is another property of a rectangle?
Answer: The diagonals are congruent.
A
quadrilateral with four congruent sides.
What is a special property of a rhombus?
Diagonals are perpendicular.
A
median is a segment from a
vertex of a triangle to the
midpoint of the opposite side.
At
a point called the
centroid
From
the vertex to the
centroid of the triangle is
2/3 the length of the
median.
 The
segment that joins the midpoints of two
sides of a triangle is parallel to the third side
and is ½ the length of the third side.
What does x equal?
3
 The
length of the segment that joins the
midpoints of the legs of a trapezoid is ½ the
length of the sum of the bases.