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Euclid Book I PROP. XXXII. -- THEOREM.

Euclid Book I PROP. XXXII. -- THEOREM.

Wednesday, Jun 24, 2020

@ Mr. Eric

If any side (AB) of a triangle (ABC) be produced (to D), the external angle (CBD) is equal to the sum of the two internal non-adjacent angles (A, C), and the sum of the three internal angles is equal to two right angles.

Euclid Book I PROP. XXIX. -- THEOREM.

Euclid Book I PROP. XXIX. -- THEOREM.

Sunday, Jun 21, 2020

@ Mr. Eric

If a right line (EF) intersect two parallel right lines (AB, CD), it makes:

  1. the alternate angles (AGH, GHD) equal to one another;
  2. the exterior angle (EGB) equal to the corresponding interior angle (GHD);
  3. the two interior angles (BGH, GHD) on the same side equal to two right angles.
Euclid Book I PROP. XXVIII. -- THEOREM.

Euclid Book I PROP. XXVIII. -- THEOREM.

Saturday, Jun 20, 2020

@ Mr. Eric

If a right line (EF) intersect two parallel right lines (AB, CD) makes the exterior angle (EGB) equal to its corresponding interior angle (GHD), or makes two interior angles (BGH, GHD) on the same side equal to two right angles, the two right lines are parallel.

Euclid Book I PROP. XXVI. -- THEOREM.

Euclid Book I PROP. XXVI. -- THEOREM.

Thursday, Jun 18, 2020

@ Mr. Eric

If two triangles (ABC, DEF) have two angles B, C) of one equal respectively to two angles (E, F) of the other, and a side of one equal to a side similarly placed with respect to the equal angles of the other, the triangles are equal in every respect.

Mr. Eric

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