Question

geometry
hw 4.1 - classifying triangles deltamath
date:
hr:
directions: use this worksheet to help you complete the deltamath online. you do not need to turn in this worksheet.

1. if c is the midpoint of bd and point e is the midpoint of df, classify each triangle as equilateral, isosceles, or scalene.

△abc:
△aef:
△adf:
△acd:

1. if qn bisects ∠pqr and n is the midpoint of pr, classify each triangle by its angles and sides.

Explanation:

Step1: Classify $\triangle ABC$

Given \(AB = 8\), \(AC=8\) (since \(C\) is the mid - point of \(BD\) and \(AB = AD\) in some relation from the figure's markings). In a triangle, if two sides are equal, it is isosceles. So, \(\triangle ABC\) is isosceles.

Step2: Classify $\triangle AEF$

Given \(AE = AE\) (common side), \(AF = 10\), \(EF=\frac{DF}{2}\) (since \(E\) is the mid - point of \(DF\) and \(DF = 10\) as \(AF = DF\) from the figure's markings). So, \(AF = DF\), \(AE\) is a median. But \(AF = 10\), \(AE\) is not equal to \(EF\). All sides are of different lengths (\(AF = 10\), \(AE
eq10\), \(EF = 5\)). So, \(\triangle AEF\) is scalene.

Step3: Classify $\triangle ADF$

Given \(AF = 10\), \(DF = 10\) (from the figure's markings), \(AD\) is related. Since \(AF = DF\), two sides are equal. So, \(\triangle ADF\) is isosceles.

Step4: Classify $\triangle ACD$

Given \(AC = AD\) (from the figure's markings), \(CD = 4\). Since two sides (\(AC\) and \(AD\)) are equal. So, \(\triangle ACD\) is isosceles.

Answer:

\(\triangle ABC\): isosceles; \(\triangle AEF\): scalene; \(\triangle ADF\): isosceles; \(\triangle ACD\): isosceles