Grade 10 · Math · Geometry

10th grade Larger angle opposite the longer side, and isosceles and equilateral triangles worksheet

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Larger angle opposite the longer side, and isosceles and equilateral triangles

Grade 10 Math Worksheet

NameDate

Circle the best answer, or write your answer on the line.

1.
Kira measures one triangle patch on a quilt, triangle DGS, with DG = 9, GS = 14, SD = 11 cm. Which list orders its angles from smallest to largest?
- ∠D, ∠S, ∠G
- ∠D, ∠G, ∠S
- ∠S, ∠D, ∠G
- ∠S, ∠G, ∠D
2.
Luz draws the top half of a kite as triangle FHU, with FH = 17, HU = 8, UF = 12 inches. Which list orders its angles from smallest to largest?
- ∠U, ∠H, ∠F
- ∠F, ∠U, ∠H
- ∠H, ∠U, ∠F
- ∠F, ∠H, ∠U
3.
Milo sketches the front of a tent as triangle QVW, with QV = 6.5, VW = 10, WQ = 5 m. Which list orders its angles from smallest to largest?
- ∠W, ∠Q, ∠V
- ∠V, ∠Q, ∠W
- ∠V, ∠W, ∠Q
- ∠Q, ∠W, ∠V
4.
Noah sketches a boat's sail as triangle CGY, with CG = 20, GY = 13, YC = 16 cm. Which list orders its angles from smallest to largest?
- ∠Y, ∠G, ∠C
- ∠C, ∠G, ∠Y
- ∠G, ∠Y, ∠C
- ∠C, ∠Y, ∠G
Pia draws the roof of a house as triangle FGH, with FG = FH, m∠G = (3x − 11)° and m∠H = (2x + 16)°. What is x?
Tala draws the side of a tower's pointed roof as triangle DQV, with DQ = DV, m∠Q = (5x − 16)° and m∠V = (3x + 20)°. What is x?
Ari draws the top half of a kite as equilateral triangle DFU, with DF = (3x + 4) cm and FU = (5x − 10) cm. What is the perimeter, in cm?
Bo measures one triangle patch on a quilt, equilateral triangle GQW, with GQ = (2x + 11) inches and QW = (4x − 5) inches. What is the perimeter, in inches?
Esme traces a wedge of cheese as equilateral triangle HSV, with HS = (6x − 5) cm and SV = (4x + 9) cm. What is the perimeter, in cm?
Jun sketches the front of a tent as equilateral triangle CDY, with CD = (7x − 8) m and DY = (5x + 4) m. What is the perimeter, in m?

10th grade Larger angle opposite the longer side, and isosceles and equilateral triangles worksheet – printable — Print: 1 2 3 4 5 6

About this worksheet

Larger angle opposite the longer side, and isosceles and equilateral triangles. Every version has 10 questions, and the answer key prints on the second page.

What your child will learn

I can name the longest side of a triangle from its angles, and order the angles from the side lengths.
I can use equal sides and equal base angles of an isosceles triangle, and the equal sides of an equilateral triangle, to find an angle, x or a perimeter.
I can solve for x when the angles are written with x, and then use the answer to order the sides or find an angle.

Standard: G-CO.C.10

Words to know

opposite (across from): The side that a corner does not touch; ∠G is across from side DF.

isosceles triangle: A triangle with two equal sides (legs), marked with the same tick.

base angles: The two angles at the ends of the base, across from the equal legs. Equal.

vertex angle: The angle between the two equal legs, at the top.

equilateral triangle: A triangle with all three sides equal; every angle is 60°.

exterior angle: The angle outside a triangle, made by extending one side.

m∠G: The measure of ∠G in degrees.

Common mistakes

Your child picked the side across from the larger angle given and did not find the third angle first.

Your child matched each angle with the side across from it but turned the order around (largest with shortest).

Your child thought the side lengths were needed to find the longest side.

What to say

Ask: what is the unmarked angle?

Ask: does a bigger angle open onto a longer side?

Ask: which angle is the biggest, and which side faces it?

Questions parents ask

What is the most common mistake with larger angle opposite the longer side, and isosceles and equilateral triangles?

Your child picked the side across from the larger angle given and did not find the third angle first.

How can I help my child with larger angle opposite the longer side, and isosceles and equilateral triangles?

Ask: what is the unmarked angle?

Are these 10th grade math worksheets free to print?

Yes. All 6 printable versions at each level are free to print, with the answer key, and no account is needed.

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