garydesir1
contestada

Determine whether the triangles are similar. If so, write a similarity statement and name the postulate or the theorem you used. If not, explain.

Determine whether the triangles are similar If so write a similarity statement and name the postulate or the theorem you used If not explain class=

Respuesta :

bcalle
a.  If two angles of one triangle are congruent to two angles of another triangle, then the triangle are similar. 
The ORDER matters in the similarity statement. The same measures must go in the same order.
∧ABC ≈ ∧PQR  Angle-Angle Similarity Postulate

b.   Set up the ratios, then reduce to see if they all reduce to the same fraction.
3/18 ; 4/24 ; 5/30
1/6   ;  1/6  ; 1/6
1/6 = 1/6 = 1/6
The sides are proportional so the triangles are proportional.
∧  ABC ≈ ∧  DEF   Side-Side-Side Similarity Postulate

According to AA postulate, triangle ABC and triangle PQR  are similar and according o the SSS postulate, triangle ABC and triangle DEF are congruent.

a)

Given :

  • In triangle ABC, [tex]\rm \angle A = 41^\circ, \;\angle B = 85^\circ,\;\angle C = 54^\circ[/tex]
  • In triangle PQR, [tex]\rm \angle P = 41^\circ, \;\angle Q = 85^\circ,\;\angle R = 54^\circ[/tex]

According to the given data:

[tex]\rm \angle A = \angle P[/tex]

[tex]\rm \angle B = \angle Q[/tex]

[tex]\rm \angle C = \angle R[/tex]

Therefore, triangle ABC and triangle PQR are similar because according to AA postulate if atleast two angles of the triangle are congruent than both the triangles are similar to each other.

b)

Given :

  • In triangle ABC, [tex]\rm AB = 4, \; BC = 5,\;CA = 3[/tex]
  • In triangle DEF, [tex]\rm DE = 24, \;EF = 30,\; FD = 18[/tex]

According to the given data, in triangle ABC and triangle DEF the ratio of:

[tex]\rm \dfrac{AB}{DE}=\dfrac{4}{24}=\dfrac{1}{6}[/tex]

[tex]\rm \dfrac{BC}{EF}=\dfrac{6}{30}=\dfrac{1}{6}[/tex]

[tex]\rm \dfrac{CA}{FD}=\dfrac{3}{18}=\dfrac{1}{6}[/tex]

Therefore, triangle ABC and triangle DEF are congruent because according to SSS postulate if all the three sides of a triangle are congruent to three sides of another triangle than both the triangles are congruent to each other.

For more information, refer the link given below:

https://brainly.com/question/19237987

Otras preguntas