Skills · Geometry · Triangles

Which postulate?

Printable practice with an answer key the engine computes, at three levels, in as many versions as you need.

Problem types

• two triangles, the equal parts marked: two sides and the angle between them marked on each: SAS
• a shared side, or vertical angles: two triangles sharing AC, with AB ≅ AD and BC ≅ DC marked: SSS
• not enough information (SSA or AAA): two sides and an angle not between them marked
• parallel sides and a diagonal: a parallelogram ABCD with its diagonal AC: AB ≅ CD marked, AB ∥ DC
• right triangles (HL, or SAS with the legs): right angles marked, the hypotenuses and one leg equal: HL

Sample Sheet · Level 1

1. 
   Which postulate proves △ABC ≅ △DEF?
2. 
   Which postulate proves △ABC ≅ △DEF?
3. 
   Which postulate proves △ABC ≅ △DEF?
4. 
   Which postulate proves △ABC ≅ △DEF?
5. 
   Which postulate proves △ABC ≅ △DEF?
6. 
   Which postulate proves △ABC ≅ △DEF?
7. 
   Which postulate proves △ABC ≅ △DEF?
8. 
   Which postulate proves △ABC ≅ △DEF?

Answer key

1. AAS: ∠A ≅ ∠D, ∠C ≅ ∠F, BC ≅ EF
2. SSS: AB ≅ DE, BC ≅ EF, AC ≅ DF
3. SAS: AC ≅ DF, ∠A ≅ ∠D, AB ≅ DE
4. ASA: ∠C ≅ ∠F, AC ≅ DF, ∠A ≅ ∠D
5. SAS: AC ≅ DF, ∠A ≅ ∠D, AB ≅ DE
6. SSS: AB ≅ DE, BC ≅ EF, AC ≅ DF
7. AAS: ∠B ≅ ∠E, ∠C ≅ ∠F, AB ≅ DE
8. ASA: ∠B ≅ ∠E, BC ≅ EF, ∠C ≅ ∠F

Sample Sheet · Level 3

1. 
   Which postulate, if any, proves △ABC ≅ △DEF?
2. 
   Which postulate, if any, proves △ABC ≅ △DEF?
3. 
   Which postulate, if any, proves △ABC ≅ △DEF?
4. 
   Which postulate, if any, proves △ABC ≅ △DEF?
5. 
   Which postulate, if any, proves △ABC ≅ △CDA?
6. 
   Which postulate, if any, proves △ABC ≅ △DEF?
7. 
   Which postulate, if any, proves △ABC ≅ △CDA?
8. 
   Which postulate, if any, proves △ABE ≅ △DCE?

Answer key

1. SAS: BC ≅ EF, ∠C ≅ ∠F, AC ≅ DF
2. HL: ∠C ≅ ∠F, AB ≅ DE, BC ≅ EF
3. not enough information
4. SSS: AB ≅ DE, BC ≅ EF, AC ≅ DF
5. ASA: ∠ACB ≅ ∠CAD, AC ≅ AC, ∠BAC ≅ ∠DCA
6. SAS: AB ≅ DE, ∠B ≅ ∠E, BC ≅ EF
7. not enough information
8. AAS: ∠A ≅ ∠D, ∠AEB ≅ ∠DEC, BE ≅ CE

Make your own

Pick the count, the level and the version, and print it with work space and the key on its own page. The same skill also makes an I Do, We Do, You Do lesson, a Mosaic, a Decoder and more.

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