Examples 3-4 Download

Transcript
EXAMPLE 3
Use the Hypotenuse-Leg Congruence Theorem
Write a proof.
GIVEN
PROVE
WY
XZ, WZ ZY, XY ZY
WYZ
XZY
SOLUTION
Redraw the triangles so they are
side by side with corresponding
parts in the same position. Mark
the given information in the
diagram.
EXAMPLE 3
Use the Hypotenuse-Leg Congruence Theorem
STATEMENTS
H 1.
WY
4.
ZY
2. Given
3. Definition of
Z and Y are
lines
right angles
WYZ and XZY are 4. Definition of a right
triangle
right triangles.
L 5. ZY
6.
1. Given
XZ
2. WZ ZY, XY
3.
REASONS
WYZ
YZ
5. Reflexive Property of
Congruence
XZY
6. HL Congruence
Theorem
EXAMPLE 4
Choose a postulate or theorem
Sign Making
You are making a canvas sign to hang on the triangular
wall over the door to the barn shown in the picture. You
think you can use two identical triangular sheets of
canvas. You know that RP QS and PQ
PS . What
postulate or theorem can you use to conclude that
PQR
PSR?
EXAMPLE 4
Choose a postulate or theorem
SOLUTION
You are given that PQ PS . By the Reflexive Property, RP
RP . By the definition of perpendicular lines, both
RPQ and RPS are right angles, so they are congruent.
So, two sides and their included angle are congruent.
ANSWER
You can use the SAS Congruence Postulate to conclude
PQR
PSR
that
.
GUIDED PRACTICE
for Examples 3 and 4
Use the diagram at the right.
3.
Redraw
ACB and
DBC side by
side with corresponding parts in the
same position.
GUIDED PRACTICE
for Examples 3 and 4
Use the diagram at the right.
4.
Use the information in the diagram to
ACB
DBC
prove that
STATEMENTS
H 1.
AB
2. AC
DC
BC, DB BC
B
REASONS
1. Given
2. Given
3. Definition of
lines
3.
C
4.
ACB and DBC are 4. Definition of a right
triangle
right triangles.
GUIDED PRACTICE
for Examples 3 and 4
STATEMENTS
REASONS
L 5. BC
5. Reflexive Property of
Congruence
6.
ACB
CB
DBC
6. HL Congruence
Theorem