Desmos or GeoGebra Challenge: Given: \(\triangle{LEA}\). Construct \(\triangle{SAM}\) so that \(\triangle{LEA}\sim\triangle{SAM}\) with a similarity ratio of \(3:5\).
1) Determine if the following statements are Always true, Sometimes true, or Never true.
a) If two triangles are similar, then they are acute.
b) Two equilateral quadrilaterals are similar.
c) Two equiangular pentagons are congruent.
d) All regular triangles are similar.
e) All octagons are similar.
2) \(\triangle{ABC}\sim\triangle{DEF}\) with \(m\angle{A}=10x^{\circ}\), \(m\angle{B}=60^{\circ}\), \(m\angle{D}=(6x-14y)^{\circ}\), and \(m\angle{F}=(8x + 3y)^{\circ}\).
a) Find \(x\) & \(y\)
b) Find the \(m\angle{C}\)
3) \(\triangle{CAR}\sim\triangle{BIK}\) with \(m\angle{C}=(7x - 6y)^{\circ}\), \(m\angle{A}=14x^{\circ}\), \(m\angle{B}=40^{\circ}\), and (m\angle{K}=(2x + 12y)^{\circ}\). Find the \(m\angle{I}\).
a) Find \(x\) & \(y\)
b) Find the \(m\angle{I}\)
1) Determine if the following statements are Always true, Sometimes true, or Never true.
a) If two triangles are similar, then they are acute.
b) Two equilateral quadrilaterals are similar.
c) Two equiangular pentagons are congruent.
d) All regular triangles are similar.
e) All octagons are similar.
2) \(\triangle{ABC}\sim\triangle{DEF}\) with \(m\angle{A}=10x^{\circ}\), \(m\angle{B}=60^{\circ}\), \(m\angle{D}=(6x-14y)^{\circ}\), and \(m\angle{F}=(8x + 3y)^{\circ}\).
a) Find \(x\) & \(y\)
b) Find the \(m\angle{C}\)
3) \(\triangle{CAR}\sim\triangle{BIK}\) with \(m\angle{C}=(7x - 6y)^{\circ}\), \(m\angle{A}=14x^{\circ}\), \(m\angle{B}=40^{\circ}\), and (m\angle{K}=(2x + 12y)^{\circ}\). Find the \(m\angle{I}\).
a) Find \(x\) & \(y\)
b) Find the \(m\angle{I}\)
5) Do you think that \(ASA\sim\) is a method used for proving similar triangles? Justify your reasoning.
9) Given \(\triangle{ABC}\), determine a composition of transformations to map onto \(\triangle{A'B'C'}\).