1. BELLRINGER Find x by using LP. 67 + x = 180. -67 -67 x = 113° x = ?
x = 113°
x = ?
y = ? y°
Lastly, use TAS to find y y = 180
 y = 23° x° 67
This is a base angle of an isosceles triangle. It must measure 67°
67°

2. What is the maximum number of congruent angles in a Scalene Triangle?
In an equilateral triangle, we already showed that all 3 angles are congruent. (60, 60, 60).
In an isosceles triangle we showed that TWO angles are congruent, the base angles.
Thus, there can be NO angles congruent in a scalene triangle, otherwise it would be isosceles or equilateral.

3. Triangle Angle-Side Relationships
You will find that the largest angle in a triangle corresponds to the longest side, and the smallest angle corresponds to the shortest side.
For example, name the sides from shortest to longest! z 60
z, x, y 68 43
q, p, r p r x y 80 52 57 q

4. In Other Words,
LONGEST
SHORTEST
SMALLEST
LARGEST

5. What is a median?
The median of a triangle connects a vertex to the opposite side’s midpoint. X Y Z
The three medians of any triangle are concurrent at the CENTROID.

6. Special segments of a triangle
Can you find the altitude, angle bisector, median, perpendicular bisector, and midsegment??
Median
Altitude
Perpendicular Bisector
Midsegment
Angle Bisector

7. Summarize our findings . . .
The angle bisectors of a triangle are concurrent at the incenter. The circle centered at the incenter is inscribed in the triangle.
The perpendicular bisectors of a triangle are concurrent at the circumcenter. The circle centered at the circumcenter circumscribes the triangle.
The altitudes of a triangle are concurrent at the orthocenter. (We will investigate the orthocenter after break).
The medians of a triangle are concurrent at the centroid. The centroid is the center of mass of the triangle.

8. Picture it all together . . .
A = altitudes
B = angle bisectors
C = medians
D = perpendicular bisectors

9. Hiding the lines . . . A = altitudes B = angle bisectors C = medians
D = perpendicular bisectors