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Identify which congruence theorem applies in each case. a. Is AAMD = ARMC? b. Is AWOH = AWAT? c. Is AGAS = AIOL? D. R. 15 cm A H. 64° 64° 15 cm 46° 72 72° G 46° d. Is AAWL = AKLW? e. Is AHOW= ATAW? f. Is ABOX ACAR? W A

Identify which congruence theorem applies in each case. a. Is AAMD = ARMC? b. Is AWOH = AWAT? c. Is AGAS = AIOL? D. R. 15 cm A H. 64° 64° 15 cm 46° 72 72° G 46° d. Is AAWL = AKLW? e. Is AHOW= ATAW? f. Is ABOX ACAR? W A

Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
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Identify which congruence theorem applies in each case

### Identifying Triangle Congruence Theorems For each pair of triangles, determine which congruence theorem applies, if any: #### a. Is \(\triangle AMD \equiv \triangle RMC\)? - **Diagram**: Two triangles sharing a vertex (\(M\)), forming an "X" shape. - \(\angle AMD\) and \(\angle RMC\) both measure \(64^\circ\). - \(AD = RC = 15 \, \text{cm}\). #### b. Is \(\triangle WOH \equiv \triangle WAT\)? - **Diagram**: Two triangles sharing the vertex \(W\). - Vertical angles \(\angle WOH\) and \(\angle WAT\) are marked as equal. #### c. Is \(\triangle GAS \equiv \triangle MOL\)? - **Diagram**: Two independent triangles. - Angles \(\angle G\) and \(\angle O\) both measure \(72^\circ\). - Angles \(\angle S\) and \(\angle L\) both measure \(40^\circ\). #### d. Is \(\triangle AWL \equiv \triangle KLW\)? - **Diagram**: Two triangles sharing a side \(WL\). #### e. Is \(\triangle AHOW \equiv \triangle TAWP\)? - **Diagram**: Two triangles sharing a common side \(AW\). #### f. Is \(\triangle BOX \equiv \triangle CAR\)? - **Diagram**: Two triangles with equal marking on sides \(BO\) and \(AC\) and \(OX\) and \(AR\). For each pair of triangles, apply the appropriate congruence theorem: Side-Angle-Side (SAS), Side-Side-Side (SSS), Angle-Side-Angle (ASA), or Angle-Angle-Side (AAS), if applicable.
Transcribed Image Text:### Identifying Triangle Congruence Theorems For each pair of triangles, determine which congruence theorem applies, if any: #### a. Is \(\triangle AMD \equiv \triangle RMC\)? - **Diagram**: Two triangles sharing a vertex (\(M\)), forming an "X" shape. - \(\angle AMD\) and \(\angle RMC\) both measure \(64^\circ\). - \(AD = RC = 15 \, \text{cm}\). #### b. Is \(\triangle WOH \equiv \triangle WAT\)? - **Diagram**: Two triangles sharing the vertex \(W\). - Vertical angles \(\angle WOH\) and \(\angle WAT\) are marked as equal. #### c. Is \(\triangle GAS \equiv \triangle MOL\)? - **Diagram**: Two independent triangles. - Angles \(\angle G\) and \(\angle O\) both measure \(72^\circ\). - Angles \(\angle S\) and \(\angle L\) both measure \(40^\circ\). #### d. Is \(\triangle AWL \equiv \triangle KLW\)? - **Diagram**: Two triangles sharing a side \(WL\). #### e. Is \(\triangle AHOW \equiv \triangle TAWP\)? - **Diagram**: Two triangles sharing a common side \(AW\). #### f. Is \(\triangle BOX \equiv \triangle CAR\)? - **Diagram**: Two triangles with equal marking on sides \(BO\) and \(AC\) and \(OX\) and \(AR\). For each pair of triangles, apply the appropriate congruence theorem: Side-Angle-Side (SAS), Side-Side-Side (SSS), Angle-Side-Angle (ASA), or Angle-Angle-Side (AAS), if applicable.
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