- EC= 42.First redraw both of the similar triangles. Since AC= AB
+BC, ACwill be:
CBC
D=E
AC
C^67 x =E^6 Cx
Since ACis six times largere than BC, ECwill be six times larger than CD.
Therefore, EC= 42.
Set 37
- ΔC.Because the two angles given in ΔA are 30° and 60°, the third
angle in ΔA is 90°. Like ΔA, choices cand ialso have angles that
measure 30°, 60°, and 90°. According to the Angle-Angle
postulate, at least two congruent angles prove similarity. To be
congruent, an included side must also be congruent. ΔA and ΔC
have congruent hypotenuses. They are congruent. - ΔI.In the previous answer, ΔC was determined to be congruent to
ΔA because of congruent sides. In ΔI, the triangle’s hypotenuse
measures 5; it has the same shape as ΔA but is smaller;
consequently, they are not congruent triangles; they are only
similar triangles. - ΔK.ΔB is an equilateral triangle. ΔH and ΔK are also equilateral
triangles (an isosceles triangle whose vertex measures 60° must also
have base angles that measure 60°). However, only ΔK and ΔBare
congruent because of congruent sides. - ΔH.ΔH has the same equilateral shape as ΔB, but they are
different sizes. They are not congruent; they are only similar.
501 Geometry Questions