Text: Drag each label to the correct location on the chart. Not all labels will be used. Given: H1 and 42 are supplementary. 42 and $3 are supplementary. Prove: I ~ $3 (I is congruent to $3). Vertical angles theorem. Congruent. Given. Complements theorem. Supplements theorem. 21 and Z2 are supplementary. 21-23. 22 and Z3 are supplementary.
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Given: H1 and 42 are supplementary. - This means that the angles H1 and 42 add up to 180 degrees. Show more…
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Key Concepts
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Write a paragraph proof of the Congruent Complements Theorem. Given: ∠1 and ∠2 are complementary. ∠2 and ∠3 are complementary. Prove: ∠1 ≅ ∠3
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Copy and complete the two-column proof for the Congruent Supplement Theorem (Theorem 2.4). Then write a paragraph proof. (See Example 5.) $\begin{array}{ll}{\text { Given }} & {\angle 1 \text { and } \angle 2 \text { are supplementary. }} \\ {} & {\angle 3 \text { and } \angle 4 \text { are supplementary. }} \\ {} & {\angle 1 \cong \angle 4} \\ {\text { Prove }} & {\angle 2 \cong \angle 3}\end{array}$
Reasoning and Proofs
Proving Geometric Relationships
Label each diagram with the given information. List any other additional information known to be true based upon a definition or property and label that in each diagram as well. Then, identify the shortcut that would prove the two triangles congruent. Use your answer and the chart on the back to color the design. MO ≅ ON, PO ≅ OQ ∠T is a right angle, SR ≅ RU ∠V ≅ ∠W, ∠X ≅ ∠U, VX ≅ WU ∠A ≅ ∠C, ∠CEG ≅ ∠AGE ∠R and ∠O are right angles, OV ≅ VR XZ ≅ DB, XB ≅ DZ FL ≅ TN, ∠L ≅ ∠T, RL ≅ HN W is the midpoint of UY, ∠U and ∠Y are right angles, UP ≅ YS C is the midpoint of ZL, ∠Z ≅ ∠L ∠P and ∠S are right angles, NS ≅ PU
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