MA.912.GR.1.2 triangle congruence
MA.912.GR.2.3
transformations
transformations
MA.912.GR.1.3Prove relationships and theorems about triangles
MA.912.GR.1.6Solve mathematical and real-world problems involving congruence
MA.912.GR.2.6
Apply rigid transformations to map one figure onto another to justify that the two figures are congruent
Apply rigid transformations to map one figure onto another to justify that the two figures are congruent
100
What theorem shows
that ΔACE congruent ΔBCD?
What is Side-Angle-Side Congruence Theorem?
100
What composition of rigid transformations maps ΔPQR to ΔXYZ?
a reflection across x = −2, then a translation 6 units right and
2 units up
100
What is m<KJL?
54 degrees
100
Select all the true statements about the figure.
A ΔFGK ≅ ΔFJK
B <GKH ≅ <JKH
C FG ≅ KG
D <GFH ≅ <JFH
E ΔGKH ≅ ΔJKH
F FG ≅ JK
A ΔFGK ≅ ΔFJK
B <GKH ≅ <JKH
D <GFH ≅ <JFH
E ΔGKH ≅ ΔJKH
100
Which triangle is congruent to ΔKLM?
ΔGJH
200
What additional piece of information is needed to show that ΔDEF is congruent to ΔPQR by the Angle-Side-Angle Congruence Theorem?
What is <D is congruent to <P?
200
What rule maps ABCD to AʹBʹCʹDʹ?
translation 1 unit left then reflection over x = 0
200
What is m<LNM?
63 degrees
200
What is m<MNT ?
120
200
If BD bisects AC and AC bisects , is ΔABE ≅ ΔCDE? Explain.
Yes; the triangles are congruent by the Side-Side-Side Congruence Theorem.
300
If <BAC ≅ <DCA, is ΔABE ≅ ΔCDE? Explain.
Yes; the triangles are congruent by the Angle-Angle-Side Congruence Theorem.
300
What are the coordinates of B′ after the pentagon is reflected across the x-axis and then rotated 90° about the origin?
(5, 1)
300
Select all the true statements if ΔABC and ΔDEF are isosceles triangles.
A The base angles of ΔABC are congruent to the base angles of ΔDEF.
B Two sides of ΔABC are congruent.
C Two angles of ΔDEF are congruent.
D Two sides of ΔABC are congruent to two sides of ΔDEF.
E ΔABC is congruent to ΔDEF.
B Two sides of ΔABC are congruent.
C Two angles of ΔDEF are congruent.
300
What is MR ?
20
300
Triangle JKL is reflected across x = 0 and then translated 5 units up to create ΔJʹKʹLʹ. Are the two figures congruent? Explain.
Yes; reflections and translations preserve lengths and angle measures, so the figures are congruent.
400
If AB is parallel to CD, is ΔACD ≅ ΔCAB? Explain.
Yes; the triangles are congruent by the Side-Angle- Side Congruence Theorem
400
What are the coordinates of E′ after the pentagon is rotated 270° about the origin and then reflected across the y-axis?
(−1, −2)
400
DF is perpendicular to GE and GE is perpendicular EH.
What is m<DFE if m<EDH = 18?
72
400
If m<BHG = 100, what is m<CED?
100
400
Select all of the following transformations that preserve distance.
A Reflection over the y-axis
B (x, y) ⟶ (6x, 6y)
C Rotation 90º clockwise about the origin
D (x, y) ⟶ (x, −y)
E Dilation with scale factor 0.5 centered at the origin
F (x, y) ⟶ (x − 8, y + 3)
A Reflection over the y-axis
C Rotation 90º clockwise about the origin
D (x, y) ⟶ (x, −y)
F (x, y) ⟶ (x − 8, y + 3)
500
Is ΔAJG ≅ ΔCDF? Explain.
Yes; both triangles are right triangles, CF≅AG , and DF≅JG , so the triangles are congruent by the Hypotenuse-Leg Congruence Theorem.
500
Given ΔABC with coordinates A (1, 3), B (4, 5), C (5, 2), what are the coordinates of ΔA′B′C′ after reflecting across the y-axis, then translating left 1 unit and up 1 unit?
A′ (-2 ,4), B′ (-5 ,6), C′ (-6 ,3)
500
DF is perpendicular to GE and GE is perpendicular EH.
What is the value of b if a = 9 and
c = 41? Round to the nearest whole number.
40
500
If m<BEF = 100 and m<CBE = 75, what is m<DAG?
25
500
Explain why ΔABC is congruent to ΔDEF. Complete the sentences. What transformations occurred?
reflect over the y-axis
translate up 2 units