Questions: AE=EC and m angle BAC=m angle DFE. AC=24 and m angle DFE=126 degrees. DF=[?]

AE=EC and m angle BAC=m angle DFE. AC=24 and m angle DFE=126 degrees. DF=[?]
Transcript text: $A E=E C$ and $m \angle B A C=m \angle D F E . A C=24$ and $m \angle D F E=126^{\circ}$. \[ \mathrm{DF}=[?] \]
failed

Solution

failed
failed

Solution Steps

Step 1: Determine if DE is a midsegment

Since AE = EC, E is the midpoint of AC. Also, since the angle at A (BAC) is congruent to the angle at F (DFE), it means that DE is parallel to BC. If a line segment's endpoint bisects a triangle's side and is parallel to the triangle's third side, then it is a midsegment. Therefore, DE is a midsegment of triangle ABC.

Step 2: Relate the length of the midsegment to the third side

The midsegment of a triangle is half as long as the third side of the triangle. In this case, the length of DE is half of BC. DE = BC/2.

Step 3: Relate the length of DF to the length of DE

Since D and F are midpoints of AB and BC respectively, DF is a midsegment of triangle ABC. Therefore, DF is half the length of AC, which is given to be 24.

Final Answer: The length of DF is 12.

Was this solution helpful?
failed
Unhelpful
failed
Helpful

Questions asked by other users

failedAnswered
learning.mheducation.com CHM1010NODA4024-General Chemistry I Question Mode: Multiple Select Q Multiple Select Question Select all that apply Which of the following statements correctly describe theoretical yield in a chemical reaction? Select all that apply. The theoretical yield considers the fact that side reactions may occur. The theoretical yield is smaller than the actual yield. The theoretical yield is the maximum amount of product that can be formed. The theoretical yield is the amount of product expected from a given amount of reactant based on the balanced chemical equation Need help? Review these concept resources. I Read About the Concept Rate your confidence to submit your answer. High Medium Low O 2024 McGraw Hill. All Rights Reserved. Privacy Center Terms of Use
failedAnswered
Relation 3 Domain Range b star r star n star f star u star
failedAnswered
Find f'(x) and simplify. f(x)=x^4 ln x Which of the following shows the correct application of the product rule? A. (x^4)(1/x)+(ln x)(4 x^3) B. (1/x)(4 x^3) C. (x^4)(4 x^3)+(ln x)(1/x) D. (x^4)(1/x)-(ln x)(4 x^3)
failedAnswered
To assess for peripheral vascular disease in the lower extremities, a nurse should: - Check for the presence of a radial pulse - Inspect for skin color and temperature changes - Evaluate respiratory function - Measure blood pressure
failedAnswered
Help Entering Answers (1 point) The distance between a point P and a line: r(t)=r0+tv can be given by: d=PR x v / v Where R is any point on the line r(t) (in particular it can be r0 ) Find the distances between the line r(t)=<-1-5t,-3-t, 3+4t> and points: 1. (5,-4,-5): 2. (2,-5,-10): 3. (4,-2,-8):