Question

Which description from the list below accuratley describe the relationship between ABC and DEF check all that apply.

Answer 1

Answer with explanation:

Given two triangles ΔABC and ΔDEF

⇒Ratio of Sides

`\rightarrow (AB)/(DE)((5)/(10))=(BC)/(EF)((3)/(6))=(AC)/(DF)((7)/(14))=(1)/(2)`

⇒Comparison of Angles

→∠A=∠D=22°

→∠B=∠E=120°

→∠C=∠F=36°

⇒As length of corresponding sides are Proportional ,as well as corresponding Angles of two triangles are same.So Two Triangles are similar either by SSS Similarity or AA Similarity or S AS Similarity.

→If Triangles are similar then they are congruent also.

→The description which accurately describe the relationship between ΔABC and ΔDEF is:

→ Option B: Similar

Answer 2

B. Similar

D. Same Shape

Explanation:

In the given triangles:

∠A ≅ ∠D = 22°

∠B ≅ ∠E = 120°

∠C ≅ ∠F = 38°

Hence using the AAA axiom of geometry

Triangle ABC and DEF are similar.

More over due to the similarity of angles the triangles also have same shape.

One more thing, that can be observed is that

DE = 2* AB

EF = 2*BC

DF = 2*AC

The sides of triangle ABC are scaled with a factor of 2 which makes it similar to DEF ..

Hence,

Option B and Option D are correct ..