Download Theorem Graphic Organizer Key

Lesson 2.3.4 Resource Page
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Theorem Graphic Organizer Key
Write theorem as a sentence:
Diagram:
V b
S
a
Side Splitter Theorem: If a segment intersects two sides of a
triangle and is parallel to the third side of the triangle, then the
lengths of the parts are proportional ( ba = dc ).
M
c
N
d
T
Converse statement (if proved):
If a segment intersects two sides of a triangle so that the lengths of
the parts are proportional ( ba = dc ), then the segment is parallel to
the third side of the triangle.
Reference:
2-110 and 2-111
Write theorem as a sentence:
Diagram:
AA ~: If two pairs of corresponding angles are
congruent, then the two triangles must be similar.
A
C
E
B
Converse statement (if proved):
F
D
If two triangles are similar, then two pairs of corresponding angles
are congruent. True because similarity is defined by
transformations, and transformations preserve angle measures.
Reference: 2-109
Write theorem as a sentence:
Diagram:
SSS ~: If all three pairs of corresponding side lengths have
the same ratio, then the two triangles must be similar.
ka
kb
kc
a
b
c
Converse statement (if proved):
Reference: 2-60
If two triangles are similar, then all three pairs of corresponding
side lengths have the same ratio. True because similarity is
defined by transformations, and dilation preserves ratios of side
lengths.
© 2015 CPM Educational Program. All rights reserved.
Core Connections Integrated II
Lesson 2.3.4 Resource Page
Page 2 of 2
Theorem Graphic Organizer Key
Write theorem as a sentence:
Diagram:
SAS ~: If two pairs of corresponding side lengths have the same
ratio, and the included angles are congruent, then the two
triangles must be similar.
ka
a
kb
b
Converse statement (if proved):
If two triangles are similar, then two pairs of corresponding side
lengths have the same ratio, and the included angles are
congruent. True because similarity is defined by
transformations, and rigid transformations preserve angle
measures and dilation preserves ratios of side lengths.
Reference:
much the same as 2-109
(given in 2-113)
Write theorem as a sentence:
Diagram:
Converse statement (if proved):
Reference:
Write theorem as a sentence:
Diagram:
Converse statement (if proved):
Reference:
© 2015 CPM Educational Program. All rights reserved.
Core Connections Integrated II