Grade 10 · Math · Geometry

10th grade Triangle proofs: fill in the missing step or reason worksheet

6 printable versionsBuilding Confidence10 questions · answer keyFree · no account

Level: Building Confidence · On Level · Challenge Me

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Triangle proofs: fill in the missing step or reason

Grade 10 Math Worksheet - Building Confidence

NameDate

Circle the best answer.

1.
Kira draws a house roof SUW whose two slopes SU and SW are equal. Which reason fills the blank?
- Converse of the base angles theorem
- Base angles theorem
- Definition of midpoint
- Given
2.
Luz cuts a pizza slice CDF from tip C to point Q on the crust. Which reason fills the blank?
- Definition of midpoint
- Given
- Definition of median
- Midsegment theorem
3.
Milo sews a seam on a triangle sail HUV from corner H to point Y on the bottom edge. Which reason fills the blank?
- Definition of median
- Definition of midpoint
- Given
- Base angles theorem
4.
Noah draws a line on a pyramid face GSW from the top G to point Q on the base. Which reason fills the blank?
- Definition of midpoint
- Definition of median
- Segment addition postulate
- Given
5.
Ren measures a triangle road sign QDH and finds its two bottom angles equal. Which reason fills the blank?
- Converse of the base angles theorem
- Base angles theorem
- Given
- Definition of isosceles triangle
6.
Tala checks a ramp's side, triangle VCS, and finds its angles at C and S equal. Which reason fills the blank?
- Given
- Converse of the base angles theorem
- Triangle angle sum theorem
- Base angles theorem
7.
Zee cuts another pizza slice DGW from tip D to point Q on the crust. Which statement fills the blank?
- GQ ≅ QW
- Q is the midpoint of DG
- DQ ⊥ GW
- Q is the midpoint of GW
8.
Bo paints a stripe UV across a pyramid face CDF, joining the middles of two sides. Which statement fills the blank?
- UV ≅ DF
- UV ∥ DF
- ∠CUV ≅ ∠CDF
- CU ≅ CV
9.
Ari hangs a string inside tent front FCH from the top F to point S on the floor. Which statement fills the blank?
- FS ⊥ CH
- CS ≅ SH
- S is the midpoint of CH
- S is the midpoint of FC
10.
Esme sews a stripe GH across a triangle sail SWY, joining the middles of two sides. Which statement fills the blank?
- SG ≅ SH
- ∠SGH ≅ ∠SWY
- GH ∥ WY
- GH ≅ WY

10th grade Triangle proofs: fill in the missing step or reason worksheet – printable — Print: 1 2 3 4 5 6

About this worksheet

Triangle proofs: fill in the missing step or reason. Every version has 10 questions, and the answer key prints on the second page.

What your child will learn

I can name the reason for each step of a proof about a triangle's angles, sides, midsegment or median.
I can tell the base angles theorem from its converse.
I can name the property of equality behind each algebra step.

Standard: G-CO.C.10

Words to know

rung: One line of the proof: a statement with its reason beside it.

Given / Prove: Given: the facts we start with. Prove: the statement the last rung must reach.

converse: The if-then turned around; it is a different statement, true or not.

base angles theorem: In a triangle with two congruent sides, the angles opposite them are congruent.

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

median: A segment from a corner to the midpoint of the opposite side.

midsegment: A segment joining the midpoints of two sides of a triangle.

parallel postulate: Through a point off a line, exactly one line is parallel to it.

Common mistakes

Your child named the converse of a theorem when the theorem itself was needed, for example the base angles theorem (equal sides give equal angles).

Your child wrote "Given" for the statement the proof is trying to reach. Only the facts on the Given line are given. Cover the Prove line and ask what is known.

Your child swapped two definitions: a median is a segment from a corner to the midpoint of the opposite side, and a midpoint splits a side into two equal halves. Draw a triangle and mark both.

What to say

Ask: which fact do we already have, the sides or the angles?

Questions parents ask

What is the most common mistake with triangle proofs: fill in the missing step or reason?

Your child named the converse of a theorem when the theorem itself was needed, for example the base angles theorem (equal sides give equal angles).

How can I help my child with triangle proofs: fill in the missing step or reason?

Ask: which fact do we already have, the sides or the angles?

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.

More geometry

See all Geometry

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