Question

Are the two triangles below similar? (5 points) Triangles GHI and JKL are shown. Angle H measures 95 degrees, angle I measures 50 degrees, side GH measures 9, side GI measures 12, angle J measures 50 degrees, angle K measures 35 degrees, side JK measures 8, side KL measures 6.
a. Yes, because the corresponding sides are proportional
b. No, because the corresponding sides are not proportional
c. Yes, because there are two pairs of congruent corresponding angles
d. No, because there are not two pairs of congruent corresponding angles

Answer 1

Let me start from the word similar

Two Shapes found in universe are said to be similar, If either they are congruent, or If they are polygons their Corresponding sides are proportional and Corresponding interior angle formed by the polygons are equal.

Now Coming to Question:

We have to check whether the two  ΔGHI  and ΔJKL are similar or not

∠H=95°, ∠I=50°,∠J=50°,∠K=35°

GH=9 ,GI=12, JK=8,KL=6

By using Angle sum property of Triangle In ΔGHI

∠G+∠H+∠I=180°

∠G=180°-50°-95°

     = 180°-145°

    = 35°

Similarly, ∠L=180° -50°-35°

 =95°

but these are not pair of Corresponding Angles.That is ∠H≠∠K, ∠G≠∠J, i.e  not congruent.

So, The two triangles,GHI and JKL are not Congruent.

Option (d) No, because there are not two pairs of congruent corresponding angles. is Correct option.

Answer 2

Answer:

I believe it is D

Step-by-step explanation:

Angles must be the same, not sides. Angel K does not match angle H.