CCSS.Math.Content.HSG-SRT.B.4
The Standard
Prove theorems about triangles.
Common Core State Standards for Mathematics
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students build proofs from triangle similarity, using angle relationships and matched side ratios. They justify when a segment inside a triangle creates proportional lengths, and when those ratios establish parallel lines. They also derive the Pythagorean relationship by drawing an altitude to a right triangle's hypotenuse.
What Mastery Looks Like
- A student labels corresponding vertices correctly and gives a reason for each similarity claim. They turn the resulting proportions into valid algebra and complete both directions of an argument about parallel lines. They can derive a² + b² = c² without assuming it first.
Common Misconceptions
- Students often assume triangles are similar because they look alike, or they match the wrong corresponding sides. Some claim lines are parallel from equal ratios without establishing the needed conditions. Others use the Pythagorean Theorem inside a proof of that same theorem, creating circular reasoning.
How to Assess It
- Exit ticket: In right triangle ABC, draw altitude CD to hypotenuse AB. Prove the two smaller triangles are similar to ABC, then use two proportions to derive AC² + BC² = AB².
Lesson moves
Ways to Teach It
Give pairs a paper triangle, ruler, and set square; they draw several parallel cross-segments, measure parts, and compare the resulting ratios.
Ask students to write: If two side-division ratios match, why must the connecting segment be parallel to the third side?
Run a proof-card sort where students order similarity statements, proportions, algebra steps, and reasons for a Pythagorean derivation.
Show a roof-truss diagram with a crossbeam parallel to the base; students calculate missing brace lengths and justify every ratio.
Free download
Printable HSG-SRT.B.4 Worksheet
A ready-to-print activity worksheet aligned to CCSS.Math.Content.HSG-SRT.B.4, with an answer key for the teacher on its own page. No account needed.
PDF, US Letter, prints cleanly in black and white.
Download the worksheetLearning progression
Where This Standard Sits
Before This Standard
If students are struggling here, check these first.
- CCSS.Math.Content.HSG-CO.C.10
Prior triangle proofs develop angle relationships and proof reasoning used when proving similarity-based triangle results.
- CCSS.Math.Content.HSG-SRT.A.3
AA similarity lets students justify similar triangles, which is essential for proving proportionality and Pythagorean theorems using similarity.
- CCSS.Math.Content.HSG-SRT.A.2
Triangle proofs here use angle equality and side proportionality from similarity to justify parallel-line and Pythagorean relationships.
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