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Can you prove the two triangles congruent? 1. A 2. G IM CE 5. 6.

Can you prove the two triangles congruent? 1. A 2. G IM CE 5. 6.

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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**Title: Do Now 6.3 - Proving Triangles Congruent** **Date: June 03, 2021** ### Can you prove the two triangles congruent? Below are six pairs of geometric figures. Your task is to determine if the two triangles in each pair are congruent. Use any of the congruence postulates (SSS, SAS, ASA, AAS, or HL) to justify your reasoning. #### Diagrams and Descriptions: 1. **Diagram 1** - **Triangles:** Triangle ADB and Triangle FCE - **Details:** Each triangle has a right angle and two pairs of corresponding sides denoted as equal (indicated by identical tick marks). 2. **Diagram 2** - **Triangles:** Triangle HJG and Triangle LKM - **Details:** Both triangles show sides marked as congruent and an angle between them denoted as equal. 3. **Diagram 3** - **Shapes:** Quadrilateral PSQR split by a diagonal SQ - **Details:** Diagonal SQ creates two triangles PSQ and SRQ within the rectangle PSQR. The sides seen in the rectangle are equal due to the properties of rectangles. 4. **Diagram 4** - **Triangles:** Triangle YWX and Triangle YVZ - **Details:** Heights and four sides are labeled with congruence marks suggesting equal lengths. 5. **Diagram 5** - **Shapes:** Quadrilateral ABDC split by a diagonal AC - **Details:** Diagonal AC divides the quadrilateral into two triangles labeling sides AD and BC with congruence marks. 6. **Diagram 6** - **Triangles:** Triangle EFG and Triangle GFH - **Details:** The triangles share side FG and have other sides marked indicating equal lengths. Consider each diagram carefully and determine if the given information is enough to prove that the triangles are congruent using the standard postulates for congruence. **Note:** If a pair of triangles cannot be proven congruent with the given information, clearly state the reason. ### Additional Resources - Review the criteria for triangle congruence postulates (SSS, SAS, ASA, AAS, HL). - Consult your textbook or class notes on congruence of triangles for further guidance.
Transcribed Image Text:**Title: Do Now 6.3 - Proving Triangles Congruent** **Date: June 03, 2021** ### Can you prove the two triangles congruent? Below are six pairs of geometric figures. Your task is to determine if the two triangles in each pair are congruent. Use any of the congruence postulates (SSS, SAS, ASA, AAS, or HL) to justify your reasoning. #### Diagrams and Descriptions: 1. **Diagram 1** - **Triangles:** Triangle ADB and Triangle FCE - **Details:** Each triangle has a right angle and two pairs of corresponding sides denoted as equal (indicated by identical tick marks). 2. **Diagram 2** - **Triangles:** Triangle HJG and Triangle LKM - **Details:** Both triangles show sides marked as congruent and an angle between them denoted as equal. 3. **Diagram 3** - **Shapes:** Quadrilateral PSQR split by a diagonal SQ - **Details:** Diagonal SQ creates two triangles PSQ and SRQ within the rectangle PSQR. The sides seen in the rectangle are equal due to the properties of rectangles. 4. **Diagram 4** - **Triangles:** Triangle YWX and Triangle YVZ - **Details:** Heights and four sides are labeled with congruence marks suggesting equal lengths. 5. **Diagram 5** - **Shapes:** Quadrilateral ABDC split by a diagonal AC - **Details:** Diagonal AC divides the quadrilateral into two triangles labeling sides AD and BC with congruence marks. 6. **Diagram 6** - **Triangles:** Triangle EFG and Triangle GFH - **Details:** The triangles share side FG and have other sides marked indicating equal lengths. Consider each diagram carefully and determine if the given information is enough to prove that the triangles are congruent using the standard postulates for congruence. **Note:** If a pair of triangles cannot be proven congruent with the given information, clearly state the reason. ### Additional Resources - Review the criteria for triangle congruence postulates (SSS, SAS, ASA, AAS, HL). - Consult your textbook or class notes on congruence of triangles for further guidance.
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