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Well if two triangles have sides of the same length, then by SSS they are congruent. In addition, if they have sides of the same length, their perimeters would be the same. So at first it seems like the answer would be yes. However, if is easy to come up with two triangles with the same perimeter whose sides do not have the same length Triangle 1 has sides 10, 15 and 30 to know if this is a triangle, we need the length of any side to be less the sum of the other two sides. So 10
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Does 2 diagonals of a square divide it into 4 congruent triangles?
0.5
Is all squares can be cut in half to make 2 congruent triangles a generalization?
no its an emphatic statement all squares can be cut in half to make 2 congruent isosceles right triangles is perhaps as general a statement as is possible
What solid figure has 2 congruent triangles for bases and 3 rectangles as faces?
A triangular prism. :)
Name four different types of triangles?
Types of Triangles: By Sides: Isosceles- 2 congruent sides Scalene- no congruent sides Equilateral- 3 congruent sides By Angles: Acute- angles measuring less than 90° Obtuse- one angle measuring more than 90° Right- one angle measuring exactly 90° Equiangular- all angles measuring exactly the same- same as equilateral triangle
What is the scale factor of the perimeters of triangle ABC and triangle WXY?
APPLYING THE SCALE FACTOR OF SIMILAR TRIANGLES TO THE PERIMETER The scale factor of two similar triangles (or any geometric shape, for that matter) is the ratio between two corresponding sides. In today's lesson, we will show that this same scale factor also applies to the ratio of the two triangles' perimeter. This is fairly easy to show, so today's lesson will be short. PROBLEM Two triangles, ΔABC and ΔADE are similar, ΔABC∼ ΔADE. The scale factor, AB/AD is 6/5. Find the ratio of the perimeters of the two triangles. Similar triangles in geometry STRATEGY We will use the definition of the scale factor to define one set of sides in terms of the other set of sides, Then, apply the definition of the perimeter. and write out the perimeter of both triangles using one set of sides. SOLUTION (1) ΔABC∼ ΔADE //Given (2) AB/AD = 6/5 //Given (3) BC/DE = 6/5 //(1), (2), scale factor is the same for all sides in similar triangles. (4) AC/AE = 6/5 //(1), (2), scale factor is the same for all sides in similar triangles. (5) AB = 6/5*AD // rearrange (2) (6) BC = 6/5*DE // rearrange (3) (7) AC = 6/5*AE // rearrange (4) (8) PABC=AB+BC+AC //definition of perimeter (9) PADE=AD+DE+AE //definition of perimeter (10)PABC=6/5AD+6/5DE+ 6/5*AE //(8), (5), (6) , (7), Transitive property of equality (11)PABC=6/5*(AD+DE+AE) //(10), Distributive property of multiplication (12) PABC=6/5*PADE //(11), (9), Transitive property of equality (13) PABC/PADE=6/5 And so we have easily shown that the scale factor of similar triangles is the same for the perimeters.
