Transcript Geometry 4.5

Warm-Up Exercises
Lesson 4.5, For use with pages 249-255
Tell whether the pair of triangles is congruent or not
and why.
ANSWER
Yes; HL
Thm.
Warm-Up1Exercises
EXAMPLE
Identify congruent triangles
Warm-Up1Exercises
EXAMPLE
Identify congruent triangles
Can the triangles be proven congruent with the
information given in the diagram? If so, state the
postulate or theorem you would use.
SOLUTION
a.
The vertical angles are congruent, so two pairs of
angles and a pair of non-included sides are
congruent. The triangles are congruent by the AAS
Congruence Theorem.
Warm-Up1Exercises
EXAMPLE
Identify congruent triangles
b.
There is not enough information to prove the
triangles are congruent, because no sides are
known to be congruent.
c.
Two pairs of angles and their included sides are
congruent. The triangles are congruent by the ASA
Congruence Postulate.
Warm-Up2Exercises
EXAMPLE
Prove the AAS Congruence Theorem
Prove the Angle-Angle-Side Congruence Theorem.
Write a proof.
GIVEN
PROVE
A
D,
ABC
C
DEF
F, BC
EF
Warm-Up
Exercises
GUIDED
PRACTICE
1.
for Examples 1 and 2
In the diagram at the right, what
postulate or theorem can you use to
RST
VUT ? Explain.
prove that
SOLUTION
STATEMENTS
REASONS
S
U
Given
RS
UV
Given
RTS
UTV
The vertical angles
are congruent
Warm-Up
Exercises
GUIDED
PRACTICE
for Examples 1 and 2
ANSWER
UTV are congruent because
Therefore RTS
vertical angles are congruent so two pairs of angles
and a pair of non included side are congruent. The
triangle are congruent by AAS Congruence Theorem.
Warm-Up
Exercises
GUIDED
PRACTICE
for Examples 1 and 2
Rewrite the proof of the Triangle Sum Theorem
on page 219 as a flow proof.
2.
ABC
GIVEN
PROVE m
1+m
2+m
3 = 180°
STATEMENTS
1. Draw BD parallel to AC .
2. m 4 + m 2 + m 5 = 180°
REASONS
1. Parallel Postulate
2. Angle Addition Postulate and
definition of straight angle
3.
1
4,
3
4. m
1= m
4,m
5. m
1+m
2+m
3. Alternate Interior Angles
5
3= m
5
3 = 180°
Theorem
4. Definition of congruent
angles
5. Substitution Property
of Equality
Warm-Up3Exercises
EXAMPLE
Write a flow proof
In the diagram, CE
BD and  CAB
Write a flow proof to show
GIVEN
PROVE
CE
BD,  CAB
ABE
ADE
ABE
CAD
CAD.
ADE
Warm-Up4Exercises
EXAMPLE
Standardized Test Practice
Warm-Up4Exercises
EXAMPLE
Standardized Test Practice
The locations of tower A, tower
B, and the fire form a triangle.
The dispatcher knows the
distance from tower A to tower B
and the measures of
A and
B. So, the measures of two
angles and an included side of
the triangle are known.
By the ASA Congruence Postulate, all triangles with these
measures are congruent. So, the triangle formed is unique
and the fire location is given by the third vertex. Two
lookouts are needed to locate the fire.
Warm-Up4Exercises
EXAMPLE
Standardized Test Practice
ANSWER
The correct answer is B.
Warm-Up
Exercises
GUIDED
PRACTICE
3.
for Examples 3 and 4
In Example 3, suppose ABE
ADE is also
given. What theorem or postulate besides ASA can
ABE
ADE?
you use to prove that
ANSWER
AAS Congruence Theorem.
Warm-Up
Exercises
GUIDED
PRACTICE
4.
for Examples 3 and 4
What If? In Example 4, suppose a fire occurs directly
between tower B and tower C. Could towers B and C
be used to locate the fire? Explain
ANSWER
No triangle is formed by the location of the fire and
towers, so the fire could be anywhere between towers B
and C.
Warm-Up Exercises
Warm-Up Exercises
Day one - 252: 1,2,4-7,9-13,18-20
Day two - 252: 14-17, 21,23-34