Download Triangle Congruence Unit

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TEKS: G2B, G8C
The student will make conjectures about
segments.
The student will use tools to determine
measurements of geometric figures
This means that the angles do not overlap.
Example: 1
Tell whether the angles are only adjacent, adjacent and
form a linear pair, or not adjacent.
AEB and BED
Adjacent and Linear Pair
AEB and BEC
Adjacent Only
DEC and AEB
Not Adjacent
Example: 2
Tell whether the angles are only adjacent, adjacent and
form a linear pair, or not adjacent.
5 and 6
Adjacent and Linear Pair
7 and SPU
Not Adjacent
7 and 8
Not Adjacent
Another angle pair relationship exists between two
angles whose sides form two pairs of opposite
rays. Vertical angles are two nonadjacent angles
formed by two intersecting lines. 1 and 3 are
vertical angles, as are 2 and 4.
Example: 3
Name the pairs of vertical angles.
HML and JMK are vertical angles.
HMJ and LMK are vertical angles.
Check
mHML  mJMK  60°.
mHMJ  mLMK  120°.
Example: 4
Name a pair of vertical angles. Do they appear to have the same
measure? Check by measuring with a protractor.
EDG and FDH are vertical angles and
appear to have the same measure.
Check mEDG ≈ mFDH ≈ 45°
Construct an angle congruent to ∡A.
A
Step 1:
Use a straight edge to draw a ray
with endpoint D.
D
B
Construct an angle
congruent to ∡A.
Step 2:
Place the compass point at A and
draw an arc that intersects both sides
of ∡ A. Label the intersections points
B and C.
D
C
A
B
Construct an angle
congruent to ∡A.
Step 3:
Using the same compass
setting, place the compass
point at D and draw an arc
that intersects the ray. Label
the intersection E.
C
A
D
E
B
Construct an angle
congruent to ∡A.
Step 4:
Place the compass point at B
and open it to the distance
BC. Tighten the compass to
keep its distance.
C
A
D
E
B
Construct an angle
congruent to ∡A.
Step 5:
Place the point of the
compass at E, without
changing its size, and draw
an arc. Label its intersection
with the first arc F.
C
F
A
D
E
B
Construct an angle
congruent to ∡A.
C
A
F
Step 6:
Use a straight edge to draw DF
D
E
Construct the bisector of ∡A.
Step 1:
Place the point of the
compass at A and draw an
arc. Label its points of
intersection with ∡A as B
and C.
A
B
A
C
Construct the bisector of ∡A.
Step 2:
Without changing the
compass setting, draw
intersecting arcs from B and
C. Label the intersection of
the arcs as D.
B
D
A
C
Construct the bisector of ∡A.
Step 3:
Use a straight edge to draw AD. AD bisects ∡A.
B
D
A
C