In this picture, we are told the measure of three angles. This is enough information to find the measure of all the angles.1) Find the measure of angles DCA, DAC and CBA.
There is also a rule in a triangle that if one angle is larger than another, the opposite side of the big angle must be longer than the opposite side of the smaller angle.
2) Use the rule to put this list of line segments in order from longest to shortest. AB, AC, AD, BC, CD.
Answers in the comments.
1) Find the measure of angles DCA, DAC and CBA.
ReplyDeleteAnswers:
measure of DCA = 110 degrees.
measure of DAC = 20 degrees.
measure of CBA = 53 degrees
There is also a rule in a triangle that if one angle is larger than another, the opposite side of the big angle must be longer than the opposite side of the smaller angle.
2) Use the rule to put this list of line segments in order from longest to shortest. AB, AC, AD, BC, CD.
Answers:
In the triangle ADC: AD > AC > CD
In the triangle ABC: AB > BC > AC
In the triangle ABD: BD > AD > AB
We can merge the inequalities together to get
AD > AB > BC > AC > CD
Not that we were asked, but BD is the longest side of all.