Transcript Transformations/Congruent Triangles Review

Ch. 3 Review
Honors Geometry
CCHS
Transformations Topics
 Find
image given a description of a
translation, reflection, or rotation.
 Find image given a function describing a
transformation. Determine if the
transformation is a translation, reflection,
rotation, or none of the above.
 Translate figures using directed line
segments.
Transformations Topics
 Reflect
over a given line.
 Rotate 90 degrees or 180 degrees around
a given point.
 Determine lines of reflectional symmetry.
 Understand the concept of rotational
symmetry.
Triangle Congruence
 Determine
if triangles can be proved
congruent by SSS, SAS, ASA, or none of
the above.
 Write basic two-column proofs proving
triangles congruent (MAKE SURE TO
INCLUDE THREE CONGRUENCE
STATEMENTS!)
 Apply properties to prove corresponding
parts of triangles congruent.
Transformations
 Give
the image if the point (-1, 5) is
translated up 2 and to the left 3.
 Give
the image if (-3, 6) is reflected over
the y axis.
 Give
the image if (-2, 5) is reflected over
the line y = 2.
Transformations
 Give
the image if (2, -5) is rotated 90
degrees clockwise about the origin.
 Give
the resulting image if the function
(x, y)  (y, -x) is applied to the point
(-1, 4). Is this a translation, reflection,
or rotation?
 Write a function that reflects a point over
the x-axis.
Transformations
Transformations
 How
many lines of
reflectional symmetry does
the figure have?
 What
is the smallest angle
about which the pentagon
has rotational symmetry?
Which rule proves the triangles
congruent?
 Given:
𝐴𝐶 𝑏𝑖𝑠𝑒𝑐𝑡𝑠 ∠𝐵𝐴𝐷
𝐴𝐶 𝑏𝑖𝑠𝑒𝑐𝑡𝑠 ∠BCD
ASA
What rule proves the triangles
congruent?
SAS
What rule proves the triangles
congruent?
Not enough
information
(SSA labeling)
What rule proves the triangles
congruent?
Given:
𝑨𝑩 ≅ 𝑩𝑪
𝑩𝑫 𝒃𝒊𝒔𝒆𝒄𝒕𝒔 < 𝑨𝑩𝑪
SAS
What rule proves the triangles
congruent?
Not enough
information
(AAS labeling)
What rule proves the triangles
congruent?
Given: < 𝑾 ≅< 𝑲
𝑾𝑽 ≅ 𝑽𝑲
ASA
One Step Proof:
Given:
< 𝑍𝑊𝑋 ≅< 𝑋𝑌𝑍
< 𝑋𝑊𝑌 ≅< 𝑍𝑌𝑊
Prove:
< 𝑍𝑊𝑌 ≅< 𝑋𝑌𝑊
Subtraction Property
One Step Proof
Given:
<1 comp. <4
<2 comp. <3
< 𝟏 ≅< 𝟐
Prove:
< 3 ≅< 4
If angles are
complementary to
congruent angles,
then they are
congruent
One Step Proof
Given:
𝑊𝑌 ≅ 𝑋𝑍
Prove:
WX ≅ YZ
Subtraction
Property
One Step Proof:
Given:
𝐷𝑀 ≅ 𝑁𝐹
M and N are mdpts
Prove:
DG ≅ FG
Multiplication
Property
Chapter 3 Tips
 Labeling
Congruent Triangles: Follow
around the perimeter of a labeled
triangle
 Review Properties (sec. 2.4-2.7 in book)
 Proofs: LABEL DIAGRAMS!!!
 Proofs: Include all labeling steps in proof
 Triangle Congruence Proofs: Make sure
you have THREE CONGRUENCE
statements! (Label S and A)
 Proofs: Make sure you have satisfied
requirements of IF statements before
including a step.