I'm going to say mostly the same thing as Ben Crowell, from just a slightly different perspective. I'm at an urban community college on the U.S. East Coast, teaching college algebra, statistics, etc. To the question, "Is there some kind of standard secondary-school geometry curriculum today?", then yes, the best answer currently is Common Core (Geometry).

Addressing a few of your specific items:

• A proof of the Pythagorean Theorem is an expected standard for earlier in the 8th grade (8.G.B.6: "Explain a proof of the Pythagorean Theorem and its converse.").
• Proofs of theorems are an expected part of high-school geometry (HSG: "Prove geometric theorems", "Prove theorems involving similarity", "Prove that all circles are similar", etc.)

In this regard, I'm modestly optimistic about what I've seen in Common Core mathematics, and that it's something of a re-alignment to solid, traditional principles. However: It's hotly debated, not implemented in all states, not yet fully implemented in the states that have signed on in the last few years, possibly not rigorously tested, not yet representative of what graduating high school students would know, etc. To the extent that schools drifted in a bunch of different directions, it would (at best) take time for Common Core to wrangle them back on a sensible path.

I will say this: Within the last year I've been giving a 1st-day introduction to all my courses including bullet points such as "This class will include proofs". As part of that I've been asking, "In what high school course did you talk about proofs a lot?", and gratifyingly every time so far I've gotten a common group shout-out of "Geometry". So for me that's actually been a bright spot recently, and a point from I can start making connections and deeper understanding.

I'm going to say mostly the same thing as Ben Crowell, from just a slightly different perspective. I'm at an urban community college on the U.S. East Coast, teaching college algebra, statistics, etc. To the question, "Is there some kind of standard secondary-school geometry curriculum today?", then yes, the best answer currently is Common Core (Geometry).

Addressing a few of your specific items:

• A proof of the Pythagorean Theorem is an expected standard for earlier in the 8th grade (8.G.B.6: "Explain a proof of the Pythagorean Theorem and its converse.").
• Proofs of theorems are an expected part of high-school geometry (HSG: "Prove geometric theorems", "Prove theorems involving similarity", "Prove that all circles are similar", etc.)

In this regard, I'm modestly optimistic about what I've seen in Common Core mathematics, and that it's something of a re-alignment to solid, traditional principles. However: It's hotly debated, not implemented in all states, not yet fully implemented in the states that have signed on in the last few years, possibly not rigorously tested, not yet representative of what graduating high school students would know, etc. To the extent that schools drifted in a bunch of different directions, it would (at best) take time for Common Core to wrangle them back on a sensible path.

I will say this: Within the last year I've been giving a 1st-day introduction to all my courses including bullet points such as "This class will include proofs". As part of that I've been asking, "In what high school course did you talk about proofs a lot?", and gratifyingly every time so far I've gotten a common group shout-out of "Geometry". So for me that's actually been a bright spot recently, and a point from which I can start making connections and deeper understanding.

I'm going to say mostly the same thing as Ben Crowell, from just a slightly different perspective. I'm at an urban community college on the U.S. East Coast, teaching college algebra, statistics, etc. To the question, "Is there some kind of standard secondary-school geometry curriculum today?", then yes, the best answer currently is Common Core (Geometry).

Addressing a few of your specific items:

• A proof of the Pythagorean Theorem is an expected standard for the 8th grade (8.G.B.6: "Explain a proof of the Pythagorean Theorem and its converse.").
• Proofs of theorems are an expected part of high-school geometry (HSG: "Prove geometric theorems", "Prove theorems involving similarity", "Prove that all circles are similar", etc.)

In this regard, I'm modestly optimistic about what I've seen in Common Core mathematics, and that it's something of a re-alignment to solid, traditional principles. However: It's hotly debated, not implemented in all states, not yet fully implemented in the states that have signed on in the last few years, possibly not rigorously tested, not yet representative of what graduating high school students would know, etc. To the extent that schools drifted in a bunch of different directions, it would (at best) take time for Common Core to wrangle them back on a sensible path.

I will say this: Within the last year I've been giving a 1st-day intro including bullet points such as "This class will include proofs". As part of that I've been asking, "Can you name a high school class with a focus on proofs?", and gratifyingly every time so far I've gotten a common group shout-out of "Geometry". So for me that's actually been a bright spot recently.

I'm going to say mostly the same thing as Ben Crowell, from just a slightly different perspective. I'm at an urban community college on the U.S. East Coast, teaching college algebra, statistics, etc. To the question, "Is there some kind of standard secondary-school geometry curriculum today?", then yes, the best answer currently is Common Core (Geometry).

Addressing a few of your specific items:

• A proof of the Pythagorean Theorem is an expected standard for earlier in the 8th grade (8.G.B.6: "Explain a proof of the Pythagorean Theorem and its converse.").
• Proofs of theorems are an expected part of high-school geometry (HSG: "Prove geometric theorems", "Prove theorems involving similarity", "Prove that all circles are similar", etc.)

In this regard, I'm modestly optimistic about what I've seen in Common Core mathematics, and that it's something of a re-alignment to solid, traditional principles. However: It's hotly debated, not implemented in all states, not yet fully implemented in the states that have signed on in the last few years, possibly not rigorously tested, not yet representative of what graduating high school students would know, etc. To the extent that schools drifted in a bunch of different directions, it would (at best) take time for Common Core to wrangle them back on a sensible path.

I will say this: Within the last year I've been giving a 1st-day introduction to all my courses including bullet points such as "This class will include proofs". As part of that I've been asking, "In what high school course did you talk about proofs a lot?", and gratifyingly every time so far I've gotten a common group shout-out of "Geometry". So for me that's actually been a bright spot recently, and a point from I can start making connections and deeper understanding.