congruence
Given: △ ABC and △ DEF
AB=DE, BC=EF and ∠ B = ∠E
are the triangles congruent? if so by which congruence rule
Yes they are congruent
by the rule : SAS
Point A is at (3,4). it is translated by the rule:
(x,y) → (x + 2 , y - 5)
what are the coordinates of point A'
A' = (5 , -1)
Given: AB = DE , BC=EF , ∠ B = ∠ E
prove: △ ABC ≅ △ DEF
by SAS
a rectangle has vertices at A(1 , 2), B(5 , 2), C(5 , 6) and D(1 , 6)
does this rectangle have a line of symmetry? if so how many
yes it does, it has 2 lines of symmetry
Given: △ XYZ and △ LMN
XY = LM, YZ = MN, XZ = LN
are the triangles congruent? if so by which congruence rule
yes they are congruent
by the rule: SSS
point B is at (-2 , 5). it is rotated 90° clockwise about the origin.
what are the coordinates of point B'
B' = (5 , 2)
Given: ∠ A = ∠ D , ∠ C = ∠ F, AC = DF
prove: △ABC ≅ △ DEF
by AAS
a regular pentagon is rotated around its center.
how many degrees can the pentagon be rotated and still look the same, what is the smallest angle of rotation?
5 lines of rotational symmetry and the smallest angle of rotation is 72°
Given: △ JLK and △ MNO
JK = MN , ∠ K = ∠ N, KL = NO
are the triangles congruent? if so by which congruence rule
Yes they are congruent
by the rule: SAS
C' = (6 , 3)
Given: AB = DE , BC = EF , AC = DF
Prove: △ ABC ≅ △ DEF
by SSS
a rhombus has a vertices at A(1 , 1), B(4 , 1), C(4 , 5) and D(1 , 5)
Does this rhombus have line symmetry? if so how many
yes the rhombus has 2 lines of symmetry
Given: △ RST and △ XYZ
∠R = ∠X , ∠S = ∠Y, RT = XZ
are the triangles congruent? if so by which congruence rule
Yes they are congruent
by the rule: AAS
Point D is at (-4 , 2). it is dilatated from the origin by a scale factor of 3 what are the coordinates of point D'
D' = (-12 , 6)
Given: ∠A = ∠ D , AB = DE , ∠B = ∠ E
Prove: △ ABC ≅ △DEF
by ASA
a regular hexagon has a vertices at A(0 , 3), B(2.6 , 2.6), C(3 , 0), D(2.6 , -2.6), E(0 , -3) and F(-2.6 , -2.6)
how many degrees can the hexagon be rotated and still look the same? and what is the smallest angle of rotation
6 lines of rotation, and the smallest angle of the rotation is 60°
Given: △ ABC and △ XYZ
∠A = ∠X , ∠B = ∠Y , ∠C = ∠Z
are the triangles congruent? if so by which congruence rule
No AAA is not a congruence rule
Point E is at (1 , 7). it is reflected over the line y = x.
what are the coordinates of the image E'
E' = (7 , 1)
Given: △ JKL and △ MNO are right triangles with hypotenuses JL = MO and JK = MN
Prove: △ JKL ≅ △ MNO
by HL
an isosceles triangle has vertices at A(0 , 0), B(4 , 6) and C(8 , 0)
does this isosceles triangle have a line of symmetry? if so how many
yes the isosceles triangle has 1 line of symmetry