Question

for numbers 10 and 11, find each measure.

Explanation:

Step1: Analyze the Diagram (Problem 11)

The figure is a trapezoid (or parallelogram - like) with segments marked as equal (E is midpoint of AB, F is midpoint of CD). We need to find a measure, likely related to the length. Given \( AE = EB \) and \( CF = FD \), and \( AD = 13 \), \( EF = 10 \). The total length of the base (or the sum of the two parallel sides) can be considered. Wait, maybe the length of \( AB \) or \( CD \)? Wait, the handwritten note has \( 10 + 13 = 23 \), then \( 23/2 = 11.5 \)? Wait, maybe the average or the length of a segment. Wait, let's re - examine. If \( EF \) is 10 and \( AD \) is 13, and E and F are midpoints, then the length of the other base (say \( BC \) or the parallel side) can be found? Wait, no, maybe the length of \( AB \) or the sum. Wait, the problem says "For numbers 10 and 11, find each measure." Let's focus on problem 11. The diagram has a quadrilateral with \( A \), \( B \), \( C \), \( D \), \( E \) on \( AB \), \( F \) on \( CD \), \( AE = EB \), \( CF = FD \), \( AD = 13 \) cm, \( EF = 10 \) cm. The formula for the length of the midline (or the segment connecting midpoints of the non - parallel sides in a trapezoid) is \( \frac{1}{2}(a + b) \), where \( a \) and \( b \) are the lengths of the two parallel sides. Wait, if \( EF \) is the midline, then \( EF=\frac{1}{2}(AD + BC) \)? Wait, no, maybe \( AD \) and \( BC \) are the parallel sides. Wait, \( AD = 13 \), \( EF = 10 \), then \( 10=\frac{1}{2}(13 + x) \), solving for \( x \): \( 20=13 + x \), \( x = 7 \)? No, the handwritten note has \( 10+13 = 23 \), \( 23/2 = 11.5 \). Maybe the length of \( AB \) or the sum of the two parallel sides divided by 2? Wait, maybe the figure is a trapezoid with \( AD \) and \( BC \) as the two parallel sides, and \( EF \) is the midline. Wait, no, the midline formula is \( \frac{a + b}{2} \). If \( EF \) is the midline, and one of the sides is 13, the other is 10? No, the handwritten calculation is \( 10 + 13=23 \), then \( 23/2 = 11.5 \). So maybe the measure is \( 11.5 \) cm.

Step2: Verify the Calculation

If we consider that the total of the two lengths (10 and 13) is 23, and we need the average (since E and F are midpoints), then \( \frac{10 + 13}{2}=\frac{23}{2}=11.5 \). So the measure is \( 11.5 \) (units, probably cm).

Answer:

\( 11.5 \) (assuming the unit is cm, based on the diagram and calculation)