Download Lesson 4.5:

Lesson 4.5:
1. Homework Discussion
2. Other Congruence Shortcuts for
Triangles
Warm Up #1:
• Do this warm up on the handout for 4.5.
• You need to use a compass and a ruler/straightedge.
• Sketch 2 equilateral triangles. The second triangle has sides
double the length of the first. Label the appropriate angle
measures on the sketch.
Warm Up #2:
• Determine the angle measures:
a)
b)
Review Work:
• Do Parts 1-3 on the In Class Review Handout.
Part 1 Questions:
• 1. Given the pair of congruent triangles, name all
corresponding congruent angles and sides.
∆𝐴𝐵𝐶 ≅ ∆𝑇𝐷𝐹
• 2. What are the two shortcuts we have learned so far to
prove that triangles are congruent?
Shortcuts:
•
There are 6 different ways that three corresponding parts of two triangles may be
congruent. Some of these will be acceptable shortcuts and some will not.
Part 2 Questions:
Part 3 Questions:
• Use deductive reasoning to decide whether or not there is enough
information to prove the triangles are congruent. If not, say, “cannot be
determined.” Use your own paper for reasoning.
a) ∆𝑋𝑌𝑊, ∆𝑍𝑊𝑌
b) ∆𝑀𝐴𝐸, ∆𝑇𝐴𝐸
Part 3 Questions:
• Use deductive reasoning to decide whether or not there is enough
information to prove the triangles are congruent. If not, say, “cannot be
determined.” Use your own paper for reasoning.
c) ∆𝐾𝐻𝐽, ∆𝐾𝐿𝐽
d) ∆𝐷𝐾𝐴, ∆𝑇𝐾𝑆
Testing AAA:
• Take a moment and think about warm up #1. Review it if
necessary.
• When two triangles have congruent angles, are they
congruent?
• AAA Congruence:
Investigation #1:
• Use the instructions on p. 227 to complete
investigation #1 only. Use your own paper or
use blank paper to do the construction. Make
sure to label it 4.5 Constructions.”
• Summarize the congruence conjecture in your
notes after the construction.
Testing ASA:
• ASA Congruence Conjecture: If two angles and
the included side of one triangle are congruent to
two angles and the included side of another
triangle, then ____________________.
SAA Congruence Conjecture:
• SAA Congruence Conjecture: If two angles and a
non-included side of one triangle are congruent
to two angles and a non-included side of another
triangle, then ____________________.
Practice:
• Do the Part 4 section on the handout.
Part 4 Questions:
• Use deductive reasoning to decide whether or not there is enough
information to prove the triangles are congruent. If not, say, “cannot be
determined.” Use your own paper for reasoning.
e) ∆𝐸𝑁𝑉, ∆𝐿𝑂𝑉
f) ∆𝑊𝑌𝑋, ∆𝑊𝑌𝑍
Part 4 Questions:
• Use deductive reasoning to decide whether or not there is enough
information to prove the triangles are congruent. If not, say, “cannot be
determined.” Use your own paper for reasoning.
g) ∆𝐶𝑅𝐷, ∆𝑅𝐶𝐴
h) ∆𝑊𝐿𝐹, ∆𝑊𝐿𝑌
Homework:
• P. 229-230: 5, 6, 8, 10, 14, 16 - 18