5.6. Comparing Angles and Sides in Triangles http://www.ck12.org
- List the sides of the two triangles in order, from least to greatest.
- Below is isosceles triangle 4 ABC. List everything you can about the triangle and why.
Answers:
- By the definition of a median,Mis the midpoint ofY Z. This means thatY M=MZ.MX=MXby the Reflexive
Property and we know thatXY>X Z. Therefore, we can use the SSS Inequality Theorem to conclude thatm^61 >
m^6 2. - Here we have no congruent sides or angles. So, let’s look at each triangle separately. Start with 4 XY Z. First the
missing angle is 42◦. The order of the sides isY Z,XY, andX Z. For 4 W X Z, the missing angle is 55◦. The order of
these sides isX Z,W Z, andW X. Because the longest side in 4 XY Zis the shortest side in 4 W X Z, we can put all the
sides together in one list:Y Z,XY,X Z,W Z,W X.
3.AB=BCbecause it is given,m^6 A=m^6 Cby the Base Angle Theorem, andAD<DCbecausem^6 ABD<m^6 CBD
and the SAS Triangle Inequality Theorem.
Interactive Practice