Download Ch 5 * Triangles and Congruence

Ch 5 – Triangles and Congruence
5.1 – Classifying Triangles
Triangle:
Parts of a triangle:
Classifying Triangles by Angles:
Classifying Triangles by Sides:
Parts of an Isosceles Triangle:
Example: Classify each triangle by its angles and by its sides.
Example: Find the measure of XY and YZ of isosceles triangle XYZ if X is the vertex angle.
5.2 – Angles of a Triangle
Theorem 5.1 – Angle Sum Theorem:
Example: Find mP in MNP if mM  80 and mN  45 .
Example: Find the value of each variable in ABC .
Theorem 5.2:
Example: Find mJ and mK in right triangle JKL.
Equiangular Triangle:
Theorem 5.3:
5.3 – Geometry in Motion
Translation:
Reflection:
Rotation:
Example: Identify each motion as translation, reflection, or rotation.
Preimage/Image
Example: In the figure, RST  XYZ by translation.
Name the image of T .
Name the side that corresponds to XY .
Example: In the figure, LMN  QRS by a rotation.
Name the image of M .
Name the angle that corresponds to S .
Name the image of LM .
Name the side that corresponds to LN .
Isometries:
Example: Identify the types of transformations that were used to complete the work.
5.4 – Congruent Triangles
Congruent Triangles:
Corresponding Parts:
Definition of Congruent Triangles:
CPCTC:
Example: If ABC  EFD , name the congruent angles and sides. Then draw the triangles, using arcs and
slash marks to show congruent angles and sides.
Example: The corresponding parts of two congruent triangles are marked in the figure. Write a congruence
statement for the two triangles.
Example: UVW is congruent to GHI . If mV  90 and mh  3x  15 , find the value of x.
5.5 – SSS and SAS
Postulate 5.1:
Example: In two triangles, DF  UV , FE  VW , and DE  UW . Write a congruence statement for the two
triangles.
Example: In two triangles, ZY  FE , XY  DE , and XZ  DF . Write the congruence statement for the two
triangles.
Included Angle:
Postulate 5.2:
Example: Determine whether the triangles are congruent. If so, write a congruence statement and explain why
the triangles are congruent. If not, explain why not.
5.6 – ASA and AAS
Included Side:
Postulate 5.3:
Example: In DEF and ABC, D  C , E  A, and DE  CA . Write a congruence statement for the two
triangles.
Theorem 5.4:
Example: XYZ and QRS each have one pair of sides and one pair of angles
marked to show congruence. What other pair of angles needs to be marked so the
two triangles are congruent by AAS?
Example: Determine whether each pair of triangles is congruent by SSS, SAS, ASA, or AAS. If it is not
possible to prove that they are congruent, write not possible.