Proving Triangle Congruence
Students will apply SSS, SAS, ASA, AAS, and HL congruence postulates to write formal proofs.
Key Questions
- Construct a two-column proof to demonstrate triangle congruence using a specific criterion.
- Differentiate between the conditions required for each triangle congruence postulate.
- Evaluate which congruence criterion is most appropriate for a given set of information.
Common Core State Standards
About This Topic
Imperialism in China during the 19th century was characterized not by direct colonial rule, but by 'Spheres of Influence' and 'Unequal Treaties.' This topic covers the Opium Wars, where Britain used military force to protect its illegal drug trade, and the subsequent carving up of China by various powers. Students also examine internal responses, such as the devastating Taiping Rebellion and the anti-foreign Boxer Rebellion.
For 10th graders, this topic explains the 'Century of Humiliation' that still informs Chinese foreign policy today. It highlights the role of economic interests in driving international conflict and the impact of the US 'Open Door Policy.' This topic particularly benefits from hands-on, student-centered approaches like a mock negotiation of an 'Unequal Treaty,' where students see the power imbalance firsthand.
Active Learning Ideas
Mock Negotiation: The Treaty of Nanjing
Students represent the British and the Qing Dynasty. The British team is given 'military advantage' cards, while the Chinese team must try to protect their sovereignty, illustrating why the resulting treaty was so one-sided.
Gallery Walk: The Boxer Rebellion
Stations feature Boxer propaganda, photos of the Eight-Nation Alliance, and the 'Boxer Protocol.' Students analyze why a group of peasants would believe they were immune to bullets and why the international response was so unified.
Think-Pair-Share: The Open Door Policy
Pairs discuss the US 'Open Door' notes. They evaluate whether this was a move to 'protect' China or simply a way for the US to ensure it wasn't left out of the Chinese market.
Watch Out for These Misconceptions
Common MisconceptionChina was colonized by the British just like India was.
What to Teach Instead
China remained technically independent but lost control over its economy and key ports (Spheres of Influence). A map activity showing 'treaty ports' versus 'colonies' helps students understand this distinction.
Common MisconceptionThe Opium Wars were about the British defending 'free trade.'
What to Teach Instead
While the British used that rhetoric, they were specifically forcing the sale of an addictive drug that was illegal in China and Britain. Peer analysis of Lin Zexu's letter to Queen Victoria helps students see the moral argument.
Suggested Methodologies
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Frequently Asked Questions
What were the Opium Wars?
What are 'Spheres of Influence'?
What was the Taiping Rebellion?
How can active learning help students understand imperialism in China?
Planning templates for Mathematics
5E Model
The 5E Model structures lessons through five phases (Engage, Explore, Explain, Elaborate, and Evaluate), guiding students from curiosity to deep understanding through inquiry-based learning.
unit plannerMath Unit
Plan a multi-week math unit with conceptual coherence: from building number sense and procedural fluency to applying skills in context and developing mathematical reasoning across a connected sequence of lessons.
rubricMath Rubric
Build a math rubric that assesses problem-solving, mathematical reasoning, and communication alongside procedural accuracy, giving students feedback on how they think, not just whether they got the right answer.
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