If ∠BAC = 17° and ∠CED = 17° are the two triangles, ΔBAC and ΔCED similar? If so, by what criterion?
2 answers:
No, not possible to tell that the the two triangles, ΔBAC and ΔCED
are similar ⇒ answer D
Step-by-step explanation:
Let us revise the cases of similarity
1. AAA similarity : two triangles are similar if all three angles in the first
triangle equal the corresponding angle in the second triangle
2. AA similarity : If two angles of one triangle are equal to the
corresponding angles of the other triangle, then the two triangles
are similar.
3. SSS similarity : If the corresponding sides of the two triangles are
proportional, then the two triangles are similar.
4. SAS similarity : In two triangles, if two sets of corresponding sides
are proportional and the included angles are equal then the two
triangles are similar.
In the two triangles BAC and CED
∵ m∠BAC = 17°
∵ m∠CED = 17°
∴ m∠BAC = m∠CED
But we need another pair of angles to prove that the two triangles are
similar by AA similarity criterion
<em>OR </em>
The lengths of sides BA , CA and CE , DE to show that
= constant ratio and prove that the
two triangles are similar by SAS similarity criterion
So it is not possible to prove that the two triangles are similar
No, not possible to tell that the the two triangles, ΔBAC and ΔCED
are similar
Learn more:
You can learn more about triangles in brainly.com/question/4354581
#LearnwithBrainly
You might be interested in
The sum of angles in any quadrilateral, including trapezoid, is 360⁰.
Because we have <span>an isosceles trapezoid, we have 2 angles with measure 135⁰,
and we have 2 equal acute angles with measure x⁰.
So, we can find value of acute angle,
135*2 +2x =360⁰
270+2x=360
2x=360-270
2x=90
x=45⁰
So, acute angles in trapezoid = 45⁰.
From triangle ABC,
angle ACB =90⁰
angle A=45⁰,
so angle ABC= 180-(90-45)=45⁰
Triangle ABC is isosceles triangle,so |AC| = |CB|= 5 in.
So, longer base AA' = 5+4+5= 14 in
Now, we can find area of trapezoid.
shorter base = 4 in
longer base = 14 in
altitude =h = 5 in
Area of trapezoid =(1/2)(base1+base2)*h
Area of trapezoid = (1/2)(4+14)*5= 9*5=45 in²
Answer is 45 in².</span>
Because we have <span>an isosceles trapezoid, we have 2 angles with measure 135⁰,
and we have 2 equal acute angles with measure x⁰.
So, we can find value of acute angle,
135*2 +2x =360⁰
270+2x=360
2x=360-270
2x=90
x=45⁰
So, acute angles in trapezoid = 45⁰.
From triangle ABC,
angle ACB =90⁰
angle A=45⁰,
so angle ABC= 180-(90-45)=45⁰
Triangle ABC is isosceles triangle,so |AC| = |CB|= 5 in.
So, longer base AA' = 5+4+5= 14 in
Now, we can find area of trapezoid.
shorter base = 4 in
longer base = 14 in
altitude =h = 5 in
Area of trapezoid =(1/2)(base1+base2)*h
Area of trapezoid = (1/2)(4+14)*5= 9*5=45 in²
Answer is 45 in².</span>