Download File

© Glencoe/McGraw-Hill
6–5
NAME
DATE
PERIOD
NAME
6–5
Study Guide
Right Triangles
DATE
PERIOD
Skills Practice
Right Triangles
Two right triangles are congruent if one of the following
conditions exist.
Determine whether each pair of right triangles is congruent by LL, HA, LA, or HL. If it is not
possible to prove that they are conguent, write not possible.
1.
2.
Theorem 6-6
LL
If two legs of one right triangle are congruent to the corresponding legs
of another right triangle, then the triangles are congruent.
Theorem 6-7
HA
If the hypotenuse and an acute angle of one right triangle are congruent
to the hypotenuse and corresponding angle of another right triangle,
then the two triangles are congruent.
If one leg and an acute angle of a right triangle are congruent to the
corresponding leg and angle of another right triangle, then the triangles
are congruent.
Postulate 6-1
HL
If the hypotenuse and a leg of one right triangle are congruent to the
hypotenuse and corresponding leg of another right triangle, then the
triangles are congruent.
F
E
W
X
Y
V
D
Z
G
A
LL
HL
3.
4.
A
R
C
A
M
State the additional information needed to prove each pair of
triangles congruent by the given theorem or postulate.
2. HA
E
T
not possible
3. LL
S C
B
HA
5.
6.
Q
R
T
A
B
C
D
(Lesson 6-5)
A12
1. HL
D
S
E
wG
E
w>F
wG
w
wB
A
w>D
wB
w
HL
wP
N
w>V
wX
w
LL
7.
Geometry: Concepts and Applications
4. LA
5. HA
8.
R
6. LA
R
A
M
Q
T
S
P
HL
M > K or
MJL > KJL
no extra information
needed
w
BC
w>D
wF
w or
A
wB
w>A
wD
w, and
BAC > DAF or
C > F
HA
9.
10.
F
C
D
I
G
LA
© Glencoe/McGraw-Hill
243
Geometry: Concepts and Applications
© Glencoe/McGraw-Hill
A
B
E
D
C
not possible
244
Answers
Theorem 6-8
LA
M
Geometry: Concepts and Applications
© Glencoe/McGraw-Hill
6–5
NAME
DATE
PERIOD
6–5
Practice
NAME
DATE
PERIOD
Reading to Learn Mathematics
Right Triangles
Right Triangles
Determine whether each pair of right triangles is congruent by LL,
HA, LA, or HL. If it is not possible to prove that they are congruent,
write not possible.
1.
2.
Key Terms
hypotenuse (hi•PA•tin•oos) in a right traingle, the side
opposite the right angle
legs in a right triangle, the two sides that form the right angle
Reading the Lesson
HA
1. Determine whether each statement is always, sometimes, or never true. If the statement is
not always true, explain why.
a. If two legs of one right triangle are congruent to the corresponding legs of another right
triangle, then the triangles are congruent. always
LL
b. If the hypotenuse and right angle of one right triangle are congruent to the
corresponding angle and hypotenuse of the other right triangle, then the triangles are
congruent. Sometimes; only if a pair of corresponding angles or a
4.
pair of corresponding legs are congruent as well.
c. If one leg and the obtuse angle of one right triangle are congruent to the corresponding
leg and angle of the other right triangle, then the triangles are congruent. Never; a
LA
LA: the triangles are right triangles and one leg
and the acute angle of one triangle are congruent
to the corresponding parts of the other triangle.
ASA: the congruent sides are included between
the congruent acute angle and the right angle. All
right angles are congruent.
HA
5.
6.
3. Use the diagram shown. Explain why you can use either LA or AAS to prove that the two
triangles are congruent.
Geometry: Concepts and Applications
not possible
LA: the two triangles are right triangles and one
leg and the acute angle of one triangle are
congruent to the corresponding parts of the other
triangle. AAS: two corresponding angles and a
non-included side are congruent. All right angles
are congruent.
LL
Helping You Remember
7.
8.
4. Describe how you can use the abbreviations LL, LA, HA, and HL to help you remember
what the three theorems and one postulate mean and how you can use them. Sample
answer: LL stands for “leg-leg.” If both pairs of corresponding legs of two
right triangles are congruent, then the triangles are congruent. LA stands
for “leg-angle.” If pairs of corresponding legs and acute angles are
congruent, then the triangles are congruent. HA stands for “hypotenuseangle.” If the corresponding hypotenuses and a pair of acute angles are
congruent, then the triangles are congruent. HL stands for “hypotenuseleg.” If the hypotenuses and a pair of corresponding legs are congruent,
then the triangles are congruent.
LA
HA
© Glencoe/McGraw-Hill
245
Geometry: Concepts and Applications
© Glencoe/McGraw-Hill
246
Geometry: Concepts and Applications
(Lesson 6-5)
A13
right triangle cannot have an obtuse angle.
2. Use the diagram shown. Explain why you can use either LA or ASA to prove that the two
triangles are congruent.
Answers
3.