The following problem is based on this theorem: “A median of a triangle separates it into two
In the figure,
a) Explain why
b) If
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Elementary Geometry For College Students, 7e
- What relationship, if any, exists between two angles a with equal measures? b that have the same vertex and a common side between them?arrow_forwardUse Exercise 33 and the following drawing to complete the proof of this theorem: The length of the median of a trapezoid is one-half the sum of the lengths of the two bases. Given: Trapezoid ABCD with median MN Prove: MN=12(AB+CD) 33. Use Theorem 5.6.1 and the drawing to complete the proof of this theorem: If a line is parallel to one side of a triangle and passes through the midpoint of a second side, then it will pass through the midpoint of the third side. Given: RST with M the midpoint of RS;MNST Prove: N is the midpoint of RTarrow_forwardIn triangle ABC, line t is drawn through vertex A in such a way that tBC. aWhich pairs of s are ? bWhat is the sum of m1, m4, and m5 ? cWhat is the sum of measures of the s of ABC ?arrow_forward
- In ABC, M is the midpoint of AB and N is the midpoint of AC. If MN= 3x-11 and BC= 4x24, find the value of x._arrow_forwarda What is the general name of the point of concurrence for the three perpendicular bisectors of the sides of a triangle? b What is the general name of the point of concurrence for the three medians of a triangle?arrow_forwardUse a two-column proof to prove the following theorem: The lengths of the corresponding altitudes of similar triangles have the same ratio as lengths of any pair of corresponding sides. Given: DEFMNP; DG and MQ are altitudes Prove: DGMQ=DEMNarrow_forward
- Does it follow from Exercise 30 that ADE is also congruent to CBE? What can you conclude regarding AE and CE in the drawing? What can you conclude regarding DEandBE?arrow_forwardConsider XYZ triangles not shown a Which side is included by X and Y?_ b Which angle is included by sides XY and YZ?_arrow_forwardIn Exercises 39 and 42, refer to the line segments shown. Use the following theorem to construct a triangle similar to the given triangle but with sides that are twice the length of those of the given triangle. Theorem: If the lengths of the three pairs of sides for two triangles are in proportion, then those triangles are similar SSS.arrow_forward
- For concave pentagon ABCDE, find the measure of the reflex angle at vertex E if mA=mD=x, mB=mC=2x, and mE=4x. HINT: E is the indicated reflex angle.arrow_forwardIn trapezoid RSTV, RSVT and MN is the median, Find the length MN if RS=12.4 in. and VT=16.2 in. _arrow_forwardIn Exercise 23 to 30, determine the value of x so that line l will be parallel to line m. m2=(x21)(x+1) m8=185x2(x+1)arrow_forward
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