Triangle congruence
Triangles are congruent if SSS, SAS, ASA, or AAS holds, or HL for right triangles.
Try it: Two triangles have three pairs of equal sides. Which rule applies?
Show answer
SSS.
Grade 10
Lessons by subject. Read the lesson, try the question, then check your answer.
Topics follow the Georgia Standards of Excellence, the state's current standards (they replaced the older Common Core Georgia Performance Standards). This is an unofficial study aid, not a Coffee County Schools resource. Your teacher's pacing guide and textbook come first. Official standards: georgiastandards.org.
Math
Congruence and Similarity
Similar triangles
Similar triangles have equal angles and proportional sides. If one triangle has sides 3, 4, 5 and a similar one has sides 6, 8, x, then x = 10.
Try it: Triangles with corresponding sides 2 and 6, and 5 and x, are similar. Find x.
Show answer
15, because the scale factor is 3.
Trigonometry and Circles
Right triangle trigonometry
SOH-CAH-TOA: sin = opposite ÷ hypotenuse, cos = adjacent ÷ hypotenuse, tan = opposite ÷ adjacent.
Try it: In a right triangle with legs 3 and 4 and hypotenuse 5, what is the sine of the angle opposite the side of length 3?
Show answer
3/5.
Circles
Circumference = 2πr and area = πr². For r = 5, C = 10π and A = 25π.
Try it: Find the area of a circle with radius 3.
Show answer
9π.
Geography
Environment and Early Civilizations
River valley civilizations
Early civilizations grew along rivers: the Nile (Egypt), the Tigris and Euphrates (Mesopotamia), the Indus, and the Yellow River (Huang He) in China.
Try it: Which river supported ancient Egypt?
Show answer
The Nile.
Trade routes
The Silk Road connected China with the Mediterranean, moving goods like silk and spices along with ideas and religions.
Try it: What traveled along the Silk Road besides goods?
Show answer
Ideas, religions, and technology.
Climate and Biomes
What shapes climate
Climate is affected by latitude, elevation, nearness to oceans, and ocean currents.
Try it: Why is it usually colder high in the mountains?
Show answer
Temperature drops as elevation increases.
Biomes
A biome is a large region with similar climate and life, such as tropical rain forest, desert, tundra, or temperate forest.
Try it: Which biome is cold and treeless?
Show answer
Tundra.
Language Arts
Reading Informational Text
Rhetorical appeals
Ethos appeals to credibility, pathos to emotion, and logos to logic.
Try it: A speaker cites statistics. Which appeal is that?
Show answer
Logos.
Evaluating sources
A credible source has an expert author, current information, evidence, and few signs of bias. Check who wrote it and why.
Try it: Name one sign that a source is credible.
Show answer
An expert author, cited evidence, or current information.
Writing
Research and synthesis
Synthesis combines ideas from several sources to support your own argument rather than just summarizing each one.
Try it: What is the difference between summary and synthesis?
Show answer
Summary restates one source. Synthesis connects several sources to make a point.
Revising for style
Use parallel structure and vary sentence length. Parallel: She likes hiking, biking, and swimming.
Try it: Make parallel: He likes to run, swim, and biking.
Show answer
He likes to run, swim, and bike.