Question 696835: The measures of the three sides of a triangle are
6, 8, and 10 centimeters. The midpoints of the
three sides are joined to form a second triangle.
How many centimeters are in the perimeter of
the second triangle?
Found 2 solutions by Alan3354, KMST:
Answer by Alan3354(69443)   (Show Source):
You can put this solution on YOUR website! The measures of the three sides of a triangle are
6, 8, and 10 centimeters. The midpoints of the
three sides are joined to form a second triangle.
How many centimeters are in the perimeter of
the second triangle?
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(6 + 8 + 10)/2 = 12 cm
Answer by KMST(5328)  (Show Source):
You can put this solution on YOUR website! I agree with Alan, but maybe it is hard to see why it is that way. Just in case, I will add a picture.
 The "second triangle" is the red triangle XYZ.
The (red) segments joining the midpoints of AB, BC, and CA split triangle ABC into 4 congruent triangles.
Each triangle is similar to ABC, and they are all half-size copies of ABC.
Their sides' lengths are 3, 4, and 5 cm.
That is obvious for the triangles that share a vertex with ABC (AZY, ZBX, and YXC) because they have two sides that are half of corresponding sides of ABC, and they have the same angle in between the corresponding sides.
The teacher would say it is SAS (side-angle-side) similarity.
Then the teacher would say that the other (red) side must also be half the size of the corresponding side in ABC.
That tells you that the red sides of XYZ also measure 3, 4, and 5 cm.
The teacher may also say that the sides of the (red) triangle XYZ are parallel to the sides of ABC, and may mention that all the triangles are right triangles, because
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