We have to determine, which of the following triangle is similar to another one.
Two similar triangle are always congruent. Two figures are similar if they have the same shape and size.
Two triangles are similar if their corresponding sides are proportional. Two polygons are similar if their corresponding side are proportional.
If two angles and the included side of one triangle are equal to the corresponding angles and side of another triangle, the triangles are congruent.
Both triangles are similar by SSS theorem, because all three pairs are in proportion,
To calculate the proportion of sides,
- Triangle 1; m1 = 67, m2 = 15
Triangle 2 ; m1 = 15 , m2 = 95
[tex]\dfrac{67}{15}= \dfrac{15}{95}[/tex]
Thus the angles are not proportion then the triangle are not similar.
- Triangle 1; m1 = 24, m2 = 101
Triangle 2 ; m1 = 65, m2 = 101
[tex]\dfrac{24}{65}= \dfrac{101}{101}[/tex]
Thus the angles are not proportion then the triangle are not similar.
- Triangle 1; m1 = 45, m2 = 80
Triangle 2 ; m1 = 59 , m2 = 45
[tex]\dfrac{45}{59}= \dfrac{80}{45}[/tex]
Thus the angles are not proportion then the triangle are not similar.
- Triangle 1; m1 = 71, m2 = 32
Triangle 2 ; m1 = 71 , m2 =77
[tex]\dfrac{71}{71}= \dfrac{32}{77}[/tex]
Thus the angles are in same proportion then the triangle are similar.
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